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== Roots == === Extraction of Roots === <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{\frac{2}{8}}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: βΒ²/β]] }}</div></div><br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{100}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: β100]] }}</div></div><br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{400}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: β400]] }}</div></div><br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{144}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: β144]] }}</div></div><br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{225}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: β225]] }}</div></div><br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{5625}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: β5625]] }}</div></div><br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{7056}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: β7056]] }}</div></div><br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{10375}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: β10375]] }}</div></div><br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{164960}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: β164960]] }}</div></div><br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{456789}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: β456789]] }}</div></div><br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{583696}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: β583696]] }}</div></div><br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{824464}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: β824464]] }}</div></div><br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{973182}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: β973182]] }}</div></div><br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{5499025}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: β5499025]] }}</div></div><br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{6169002849}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: β6169002849]] }}</div></div><br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{344680129066}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: β344680129066]] }}</div></div><br> === Extraction of Cube Roots === <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{\frac{8}{27}}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: Β³β(βΈ/ββ)]] }}</div></div><br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{\frac{1}{5}}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: Β³β(β )]] }}</div></div><br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{\frac{1}{2}}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: Β³β(Β½)]] }}</div></div><br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{1+\frac{1}{2}}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: Β³β(1+Β½)]] }}</div></div><br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{2+\frac{1}{2}}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: Β³β(2+Β½)]] }}</div></div><br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{2+\frac{10}{27}}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: Β³β(2+ΒΉβ°/ββ)]] }}</div></div><br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{3+\frac{3}{27}}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: Β³β(3+Β³/ββ)]] }}</div></div><br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{3+\frac{1}{4}}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: Β³β(3+ΒΌ)]] }}</div></div><br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{10}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: Β³β10]] }}</div></div><br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{15}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: Β³β15]] }}</div></div><br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{10000}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: Β³β10000]] }}</div></div><br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{12167}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: Β³β12167]] }}</div></div><br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{571787}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: Β³β571787]] }}</div></div><br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{1072000}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: Β³β1072000]] }}</div></div><br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{12812904}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: Β³β12812904]] }}</div></div><br> === Approximation === <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{2}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: β2]] }}</div></div><br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{20}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: β20]] }}</div></div><br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{200}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: β200]] }}</div></div><br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{2000}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: β2000]] }}</div></div><br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{20000}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: β20000]] }}</div></div><br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{4000}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: β4000]] }}</div></div><br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{5}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: β5]] }}</div></div><br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{10}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: β10]] }}</div></div><br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{15}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: β15]] }}</div></div><br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{6}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: β6]] }}</div></div><br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{7}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: β7]] }}</div></div><br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{18}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: β18]] }}</div></div><br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{29}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: β29]] }}</div></div><br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{925}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: β925]] }}</div></div><br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{76543}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: β76543]] }}</div></div><br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{6169004404}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: β6169004404]] }}</div></div><br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{\frac{4}{6}\sdot\left(4+\frac{5}{9}\right)}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #root[0] ]] [[comment: β(β΄/βΒ·(4+β΅/β))]] }}</div></div><br> === Addition of Roots === <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{9}+\sqrt{4}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #addition of roots]] [[comment: β9+β4]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{10}+\sqrt{2}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #addition of roots]] [[comment: β10+β2]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{3}+\sqrt{12}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #addition of roots]] [[comment: β3+β12]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{6}+\sqrt{7}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #addition of roots]] [[comment: β6+β7]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{12}+\sqrt{48}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #addition of roots]] [[comment: β12+β48]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{18}+\sqrt{8}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #addition of roots]] [[comment: β18+β8]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{8}+\sqrt{19}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #addition of roots]] [[comment: β8+β19]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{16}+\sqrt{36}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #addition of roots]] [[comment: β16+β36]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle2\sdot\sqrt{9}+3\sdot\sqrt{16}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #addition of roots]] [[comment: 2β9+3β16]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\sdot\sqrt{9}+\frac{3}{4}\sdot\sqrt{16}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #addition of roots]] [[comment: β β9+ΒΎβ16]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{96}+\sqrt[3]{324}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #addition of roots]] [[comment: Β³β96+Β³β324]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4+\sqrt{12}\right)+\left(5+\sqrt{3}\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #addition of roots]] [[comment: (4+β12)+(5+β3)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4+\sqrt{3}\right)+\left(\sqrt{12}-3\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #addition of roots]] [[comment: (4+β3)+(β12-3)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4+\sqrt{3}\right)+\left(\sqrt{12}-2\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #addition of roots]] [[comment: (4+β3)+(β12-2)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4-\sqrt{3}\right)+\left(\sqrt{12}-2\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #addition of roots]] [[comment: (4-β3)+(β12-2)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{3}+\sqrt{6}+\sqrt{12}+\sqrt{24}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #addition of roots]] [[comment: β3+β6+β12+β24]] }}</div></div> <br> === Subtraction of Roots === <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{9}-\sqrt{4}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #subtraction of roots]] [[comment: β9-β4]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{16}-\sqrt{9}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #subtraction of roots]] [[comment: β16-β9]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{12}-\sqrt{3}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #subtraction of roots]] [[comment: β12-β3]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{18}-\sqrt{8}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #subtraction of roots]] [[comment: β18-β8]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{7}-\sqrt{6}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #subtraction of roots]] [[comment: β7-β6]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{36}-\sqrt{16}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #subtraction of roots]] [[comment: β36-β16]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle3\sdot\sqrt{36}-2\sdot\sqrt{16}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #subtraction of roots]] [[comment: 3β36-2β16]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\sdot\sqrt{36}-\frac{1}{2}\sdot\sqrt{16}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #subtraction of roots]] [[comment: β β36-Β½β16]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle19-\left(10-\sqrt{12}\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #subtraction of roots]] [[comment: 19-(10-β12)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle10-\left(24-\sqrt{250}\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #subtraction of roots]] [[comment: 10-(24-β250)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle16-\left(8+\sqrt{50}\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #subtraction of roots]] [[comment: 16-(8+β50)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(13-\sqrt{20}\right)-\left(6-\sqrt{5}\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #subtraction of roots]] [[comment: (13-β20)-(6-β5)]] }}</div></div> <br> === Multiplication of Roots === <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{9}\times\sqrt{4}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: β9Γβ4]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{4}\times\sqrt{9}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: β4Γβ9]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{7}\times\sqrt{8}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: β7Γβ8]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{5}\times\sqrt{12}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: β5Γβ12]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{9}\times\sqrt{36}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: β9Γβ36]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\sdot\sqrt{9}\times3\sdot\sqrt{36}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: 4β9Γ3β36]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\sdot\sqrt{9}\times\frac{1}{2}\sdot\sqrt{36}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: β β9ΓΒ½β36]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle2\times\sqrt{16}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: 2Γβ16]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\times\sqrt{9}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: 4Γβ9]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{2}\times\sqrt{9}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: Β½Γβ9]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}\times\sqrt{9}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: β Γβ9]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\times\sqrt{9}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: β Γβ9]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{6}\times3</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: β6Γ3]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{7}\times3</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: β7Γ3]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{7}\times8</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: β7Γ8]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{5}\times\left(\sqrt{7}+4\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: β5Γ(β7+4)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{3}\times\left(6-\sqrt{8}\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: β3Γ(6-β8)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\sqrt{5}\right)\times\left(3+\sqrt{5}\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: (3+β5)Γ(3+β5)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(5+\sqrt{6}\right)\times\left(5+\sqrt{6}\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: (5+β6)Γ(5+β6)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\sqrt{5}\right)\times\left(4+\sqrt{7}\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: (3+β5)Γ(4+β7)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\sqrt{4}\right)\times\left(4+\sqrt{9}\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: (3+β4)Γ(4+β9)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3-\sqrt{5}\right)\times\left(4-\sqrt{7}\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: (3-β5)Γ(4-β7)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3-\sqrt{5}\right)\times\left(3-\sqrt{5}\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: (3-β5)Γ(3-β5)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(5+\sqrt{3}\right)\times\left(5-\sqrt{3}\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: (5+β3)Γ(5-β3)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\sqrt{4}\right)\times\left(5-\sqrt{9}\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: (3+β4)Γ(5-β9)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{8}\times\left(\sqrt{8}-2\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: β8Γ(β8-2)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{8}-2\right)\times\left(\sqrt{10}-3\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: (β8-2)Γ(β10-3)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{12}-2\right)\times\left(\sqrt{12}-2\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: (β12-2)Γ(β12-2)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{32}-3\right)\times\left(\sqrt{32}-3\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: (β32-3)Γ(β32-3)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{15}-3\right)\times\left(\sqrt{12}+2\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: (β15-3)Γ(β12+2)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{8}+2\right)\times\left(\sqrt{8}-2\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: (β8+2)Γ(β8-2)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(2\times\sqrt{10}\right)\times\left(\frac{1}{2}\times\sqrt{5}\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: (2Γβ10)Γ(Β½Γβ5)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{5}\times\left(\sqrt{7}+\sqrt{10}\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: β5Γ(β7+β10)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{5}\times\left(\sqrt{12}-\sqrt{8}\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: β5Γ(β12-β8)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{5}+\sqrt{7}\right)\times\left(\sqrt{10}+\sqrt{15}\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: (β5+β7)Γ(β10+β15)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{5}+\sqrt{7}\right)\times\left(\sqrt{5}+\sqrt{7}\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: (β5+β7)Γ(β5+β7)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{5}+\sqrt{7}\right)\times\left(\sqrt{10}-\sqrt{6}\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: (β5+β7)Γ(β10-β6)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{10}+\sqrt{7}\right)\times\left(\sqrt{10}-\sqrt{7}\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: (β10+β7)Γ(β10-β7)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{8}+\sqrt{4}\right)\times\left(\sqrt{8}-\sqrt{4}\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: (β8+β4)Γ(β8-β4)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{48}+\sqrt{10}\right)\times\left(\sqrt{48}-\sqrt{10}\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: (β48+β10)Γ(β48-β10)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{12}-\sqrt{7}\right)\times\left(\sqrt{15}-\sqrt{10}\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: (β12-β7)Γ(β15-β10)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{12}-\sqrt{7}\right)\times\left(\sqrt{12}-\sqrt{7}\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: (β12-β7)Γ(β12-β7)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle3\times\sqrt{4}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: 3Γβ4]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle3\times\sqrt[3]{8}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: 3ΓΒ³β8]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle3\times\sqrt[3]{5}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: 3ΓΒ³β5]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{4}\times\sqrt[3]{8}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: β4ΓΒ³β8]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{9}\times\sqrt[3]{8}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: β9ΓΒ³β8]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{5}\times\sqrt[3]{6}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: Β³β5ΓΒ³β6]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle2\times\sqrt[4]{5}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: 2Γβ΄β5]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{8}\times\sqrt[4]{16}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: Β³β8Γβ΄β16]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{3}\times\sqrt[4]{4}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: Β³β3Γβ΄β4]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[4]{4}\times\sqrt[4]{7}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: β΄β4Γβ΄β7]] }}</div></div> <br> === Division of Roots === <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{9}\div\sqrt{4}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #division of roots]] [[comment: β9Γ·β4]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{4}\div\sqrt{9}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #division of roots]] [[comment: β4Γ·β9]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{10}\div\sqrt{2}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #division of roots]] [[comment: β10Γ·β2]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{30}\div\sqrt{6}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #division of roots]] [[comment: β30Γ·β6]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{36}\div\sqrt{9}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #division of roots]] [[comment: β36Γ·β9]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle5\sdot\sqrt{9}\div2\sdot\sqrt{36}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #division of roots]] [[comment: 5β9Γ·2β36]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\sdot\sqrt{36}\div\frac{2}{3}\sdot\sqrt{9}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #division of roots]] [[comment: β β36Γ·β β9]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\div\sqrt{9}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #division of roots]] [[comment: 4Γ·β9]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle12\div\sqrt{4}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #division of roots]] [[comment: 12Γ·β4]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle20\div\sqrt{10}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #division of roots]] [[comment: 20Γ·β10]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle8\div\left(3+\sqrt{4}\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #division of roots]] [[comment: 8Γ·(3+β4)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle19\div\left(2+\sqrt{16}\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #division of roots]] [[comment: 19Γ·(2+β16)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{64}\div\left(\sqrt{8}-\sqrt{4}\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #division of roots]] [[comment: β64Γ·(β8-β4)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{64}\div\left(\sqrt{8}+\sqrt{4}\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #division of roots]] [[comment: β64Γ·(β8+β4)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(5+\sqrt{16}\right)\div3</math><div class="mw-collapsible-content"> {{#annotask: [[category: #division of roots]] [[comment: (5+β16)Γ·3]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle20\div\left(4-\sqrt{9}\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #division of roots]] [[comment: 20Γ·(4-β9)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(19+\sqrt{25}\right)\div\left(5+\sqrt{9}\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #division of roots]] [[comment: (19+β25)Γ·(5+β9)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(2\times\sqrt{20}\right)\div\left(3\times\sqrt{6}\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #division of roots]] [[comment: (2Γβ20)Γ·(3Γβ6)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle36\div\left(\sqrt{4}+\sqrt{9}+\sqrt{16}\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #division of roots]] [[comment: 36Γ·(β4+β9+β16)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle70\div\left(\sqrt{4}+\sqrt{9}+\sqrt{16}+\sqrt{25}\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #division of roots]] [[comment: 70Γ·(β4+β9+β16+β25)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{6}\div\sqrt[3]{10}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #division of roots]] [[comment: β6Γ·Β³β10]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{18}\div\sqrt[4]{10}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #division of roots]] [[comment: Β³β18Γ·β΄β10]] }}</div></div> <br>
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