Mathematical formula

$\scriptstyle\left(3n+1\right)^2=\left[\left[10\sdot\left[\frac{1}{3}\sdot\left(3n\right)\right]^2\right]-\left[\frac{1}{3}\sdot\left(3n\right)\right]^2\right]+3n+\left(3n+1\right)$

Roots

Addition of Roots

[Expand]$\scriptstyle\sqrt{3}+\sqrt{12}$

no such category found: #R+R

[Expand]$\scriptstyle\sqrt{6}+\sqrt{7}$

no such category found: #R+R

[Expand]$\scriptstyle\sqrt{12}+\sqrt{48}$

no such category found: #R+R

[Expand]$\scriptstyle\sqrt{8}+\sqrt{19}$

no such category found: #R+R

[Expand]$\scriptstyle\left(4+\sqrt{12}\right)+\left(5+\sqrt{3}\right)$

no such category found: #(N+R)+(N+R)

[Expand]$\scriptstyle\left(4+\sqrt{3}\right)+\left(\sqrt{12}-3\right)$

no such category found: #(N+R)+(R-N)

[Expand]$\scriptstyle\left(4+\sqrt{3}\right)+\left(\sqrt{12}-2\right)$

no such category found: #(N+R)+(R-N)

[Expand]$\scriptstyle\left(4-\sqrt{3}\right)+\left(\sqrt{12}-2\right)$

no such category found: #(N-R)+(R-N)

[Expand]$\scriptstyle\sqrt{3}+\sqrt{6}+\sqrt{12}+\sqrt{24}$

no such category found: #R+R+R+R

Subtraction of Roots

[Expand]$\scriptstyle\sqrt{12}-\sqrt{3}$

no such category found: #R-R

[Expand]$\scriptstyle\sqrt{18}-\sqrt{8}$

no such category found: #R-R

[Expand]$\scriptstyle\sqrt{7}-\sqrt{6}$

no such category found: #R-R

[Expand]$\scriptstyle19-\left(10-\sqrt{12}\right)$

no such category found: #N-(N-R)

[Expand]$\scriptstyle10-\left(24-\sqrt{250}\right)$

no such category found: #N-(N-R)

[Expand]$\scriptstyle16-\left(8+\sqrt{50}\right)$

no such category found: #N-(N+R)

[Expand]$\scriptstyle\left(13-\sqrt{20}\right)-\left(6-\sqrt{5}\right)$

no such category found: #(N-R)-(N-R)

Multiplication of Roots

[Expand]$\scriptstyle\sqrt{4}\times\sqrt{9}$

no such category found: #R×R

[Expand]$\scriptstyle\sqrt{5}\times\sqrt{12}$

no such category found: #R×R

[Expand]$\scriptstyle\sqrt{6}\times3$

no such category found: #R×N

[Expand]$\scriptstyle\sqrt{7}\times3$

no such category found: #R×N

[Expand]$\scriptstyle\sqrt{5}\times\left(\sqrt{7}+4\right)$

no such category found: #R×(R+N)

[Expand]$\scriptstyle\sqrt{3}\times\left(6-\sqrt{8}\right)$

no such category found: #R×(N-R)

[Expand]$\scriptstyle\left(3+\sqrt{5}\right)\times\left(3+\sqrt{5}\right)$

no such category found: #(N+R)×(N+R)

[Expand]$\scriptstyle\left(3+\sqrt{5}\right)\times\left(4+\sqrt{7}\right)$

no such category found: #(N+R)×(N+R)

[Expand]$\scriptstyle\left(3+\sqrt{4}\right)\times\left(4+\sqrt{9}\right)$

no such category found: #(N+R)×(N+R)

[Expand]$\scriptstyle\left(3-\sqrt{5}\right)\times\left(4-\sqrt{7}\right)$

no such category found: #(N-R)×(N-R)

[Expand]$\scriptstyle\left(3-\sqrt{5}\right)\times\left(3-\sqrt{5}\right)$

no such category found: #(N-R)×(N-R)

[Expand]$\scriptstyle\left(5+\sqrt{3}\right)\times\left(5-\sqrt{3}\right)$

no such category found: #(N+R)×(N-R)

[Expand]$\scriptstyle\left(3+\sqrt{4}\right)\times\left(5-\sqrt{9}\right)$

no such category found: #(N+R)×(N-R)

[Expand]$\scriptstyle\sqrt{8}\times\left(\sqrt{8}-2\right)$

no such category found: #R×(R-N)

[Expand]$\scriptstyle\left(\sqrt{8}-2\right)\times\left(\sqrt{10}-3\right)$

no such category found: #(R-N)×(R-N)

[Expand]$\scriptstyle\left(\sqrt{12}-2\right)\times\left(\sqrt{12}-2\right)$

no such category found: #(R-N)×(R-N)

[Expand]$\scriptstyle\left(\sqrt{15}-3\right)\times\left(\sqrt{12}+2\right)$

no such category found: #(R-N)×(R+N)

[Expand]$\scriptstyle\left(\sqrt{8}+2\right)\times\left(\sqrt{8}-2\right)$

no such category found: #(R+N)×(R-N)

[Expand]$\scriptstyle\sqrt{5}\times\left(\sqrt{7}+\sqrt{10}\right)$

no such category found: #R×(R+R)

[Expand]$\scriptstyle\sqrt{5}\times\left(\sqrt{12}-\sqrt{8}\right)$

no such category found: #R×(R-R)

[Expand]$\scriptstyle\left(\sqrt{5}+\sqrt{7}\right)\times\left(\sqrt{10}+\sqrt{15}\right)$

no such category found: #(R+R)×(R+R)

[Expand]$\scriptstyle\left(\sqrt{5}+\sqrt{7}\right)\times\left(\sqrt{5}+\sqrt{7}\right)$

no such category found: #(R+R)×(R+R)

[Expand]$\scriptstyle\left(\sqrt{5}+\sqrt{7}\right)\times\left(\sqrt{10}-\sqrt{6}\right)$

no such category found: #(R+R)×(R-R)

[Expand]$\scriptstyle\left(\sqrt{10}+\sqrt{7}\right)\times\left(\sqrt{10}-\sqrt{7}\right)$

no such category found: #(R+R)×(R-R)

[Expand]$\scriptstyle\left(\sqrt{48}+\sqrt{10}\right)\times\left(\sqrt{48}-\sqrt{10}\right)$

no such category found: #(R+R)×(R-R)

[Expand]$\scriptstyle\left(\sqrt{12}-\sqrt{7}\right)\times\left(\sqrt{15}-\sqrt{10}\right)$

no such category found: #(R-R)×(R-R)

[Expand]$\scriptstyle\left(\sqrt{12}-\sqrt{7}\right)\times\left(\sqrt{12}-\sqrt{7}\right)$

no such category found: #(R-R)×(R-R)

[Expand]$\scriptstyle3\times\sqrt{4}$

no such category found: #N×R

[Expand]$\scriptstyle3\times\sqrt[3]{8}$

no such category found: #N×R₃

[Expand]$\scriptstyle\sqrt{4}\times\sqrt[3]{8}$

no such category found: #R×R₃

[Expand]$\scriptstyle\sqrt[3]{8}\times\sqrt[4]{16}$

no such category found: #R₃×R₄

Division of Roots

[Expand]$\scriptstyle\sqrt{4}\div\sqrt{9}$

no such category found: #R÷R

[Expand]$\scriptstyle4\div\sqrt{9}$

no such category found: #N÷R

[Expand]$\scriptstyle8\div\left(3+\sqrt{4}\right)$

no such category found: #N÷(N+R)

[Expand]$\scriptstyle19\div\left(2+\sqrt{16}\right)$

no such category found: #N÷(N+R)

[Expand]$\scriptstyle\left(5+\sqrt{16}\right)\div3$

no such category found: #(N+R)÷N

[Expand]$\scriptstyle20\div\left(4-\sqrt{9}\right)$

no such category found: #N÷(N-R)

[Expand]$\scriptstyle\left(19+\sqrt{25}\right)\div\left(5+\sqrt{9}\right)$

no such category found: #(N+R)÷(N+R)

[Expand]$\scriptstyle36\div\left(\sqrt{4}+\sqrt{9}+\sqrt{16}\right)$

no such category found: #N÷(R+R+R)

[Expand]$\scriptstyle70\div\left(\sqrt{4}+\sqrt{9}+\sqrt{16}+\sqrt{25}\right)$

no such category found: #N÷(R+R+R+R)

Linear Equation

[Expand]$\scriptstyle bx=\sqrt[3]{c}$

Category	Comment	Link	Annotated text
equation/linear equation	bx=³√c	ספר_ג'יבלי_אלמוקבאלא#NHZd	When things are equal to a cube root of the numbers: :$\scriptstyle bx=\sqrt[3]{c}$ כאשר הדברי' יהיו שוי' אל שרש מעוק' ממספרי‫'

[Expand]$\scriptstyle c=\sqrt[3]{bx}$

Category	Comment	Link	Annotated text
equation/linear equation	c=³√bx	ספר_ג'יבלי_אלמוקבאלא#jGFm	When numbers are equal to a cube root of a thing: :$\scriptstyle c=\sqrt[3]{bx}$ כאשר המספרי' יהיו שוים אל שרש מעו' מדבר

Quadratic Equation

[Expand]$\scriptstyle ax^2=\sqrt[3]{c}$

Category	Comment	Link	Annotated text
equation/quadratic equation	ax²=³√c	ספר_ג'יבלי_אלמוקבאלא#rGD5	When squares are equal to a cube root of the numbers: :$\scriptstyle ax^2=\sqrt[3]{c}$ כאשר הצינסי יהיו שוים אל שרשי' מעו' ממספרי‫'

[Expand]$\scriptstyle c=\sqrt[3]{ax^2}$

Category	Comment	Link	Annotated text
equation/quadratic equation	c=³√ax²	ספר_ג'יבלי_אלמוקבאלא#zK2y	When numbers are equal to a cube root of squares: :$\scriptstyle c=\sqrt[3]{ax^2}$ כאשר המספרי' יהיו שוים אל שרשי' מעו' מצינסי

Cubic Equation

[Expand]$\scriptstyle ax^3=\sqrt[3]{c}$

Category	Comment	Link	Annotated text
equation/cubic equation	ax³=³√c	ספר_ג'יבלי_אלמוקבאלא#eOI5	It is when cubes are equal to a cube root of the numbers: :$\scriptstyle ax^3=\sqrt[3]{c}$ וזהו כאשר המעוקבי' יהיו שוים אל שרש מעו' ממספרי‫'

Biquadratic Equation

[Expand]$\scriptstyle4\sdot\left(x^2+8\right)=x^4$

Category	Comment	Link	Annotated text
quartic equation/biquadratic equation	4(x²+8)=x⁴	אגרת_המספר#q2Fw	6) $\scriptstyle4\sdot\left(x^2+8\right)=\left(x^2\right)^2$ הששית ממון הוספת עליו ח' זוזים והכית המקובץ בארבעה והיה היוצא הכאת הממון בעצמו
quartic equation/biquadratic equation	4(x²+8)=x⁴	תחבולות_המספר#G1Mq	[6] He said: the six problem is as if you are told: we add to a certain square [eight] dirham, then multiply the sum by four dirham and the result is the same as the product of the square [by itself]. :$\scriptstyle4\sdot\left(X^2+8\right)=\left(X^2\right)^2$ אמ' והשאלה הששית כמו אם יאמרו לך הוספנו על התמונ' מרובע מה שלשה דרהמי והכינו המקובץ בארבעה דרהמי והיה העולה כמו הכאת א"ב בעצמו המרובע
quartic equation/biquadratic equation	4(x²+8)=x⁴	חשבון_השטחים#ZxMx	$\scriptstyle4\sdot\left(X^2+8\right)=\left(X^2\right)^2$ אלגו תוסיף עליו שמנה אדרהם ותכה {{#annot:term|388,1217|vQSL}}המקובץ{{#annotend:vQSL}} על ארבעה אדרהם והיה כמו האלגו על עצמו

[Expand]$\scriptstyle c=ax^4+\sqrt{bx^4}$

Category	Comment	Link	Annotated text
quartic equation/biquadratic equation	c=ax⁴+√(bx⁴)	ספר_ג'יבלי_אלמוקבאלא#h9il	When numbers are equal to squares of squares and a root of squares of squares: :$\scriptstyle c=ax^4+\sqrt{bx^4}$ כאשר המספרי' יהיו שוים אל הצינסי מצינסי ואל שרשי צינסי מצינסי

[Expand]$\scriptstyle ax^4+bx^2=c$

Category	Comment	Link	Annotated text
quartic equation/biquadratic equation	ax⁴+bx²=c	ספר_ג'יבלי_אלמוקבאלא#Tu7N	When squares of squares plus squares are equal to a number: :$\scriptstyle ax^4+bx^2=c$ כאשר הצינסי מצינסי וצינסי יהיו שוים אל מספר

[Expand]$\scriptstyle bx^2=ax^4+c$

Category	Comment	Link	Annotated text
quartic equation/biquadratic equation	bx²=ax⁴+c	ספר_ג'יבלי_אלמוקבאלא#tkSO	When squares are equal to squares of squares and a root of a number: :$\scriptstyle bx^2=ax^4+c$ כאשר הצינסי יהיו שוים אל הצינסי מצינסי ואל מספר

[Expand]$\scriptstyle ax^4=bx^2+c$

Category	Comment	Link	Annotated text
quartic equation/biquadratic equation	ax⁴=bx²+c	ספר_ג'יבלי_אלמוקבאלא#CLbn	When squares of squares are equal to a number and squares: :$\scriptstyle ax^4=bx^2+c$ כאשר הצינסי מצינסי יהיו שוים אל המספר והצינסי