Math Formulas Search

1.

Root of a product

$\sqrt{ab}=\sqrt{a}\sqrt{b}$

2.

Root of a fraction

$\sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}$

3.

Root of a square

$\sqrt{a^2} = |a|$

4.

Square of a root

$\left(\sqrt{a}\right)^2=a$

5.

Rationalise denominator

$\dfrac{1}{\sqrt{a}}=\dfrac{\sqrt{a}}{a}$

6.

Rationalise denominator

$\dfrac{1}{\sqrt{a}+\sqrt{b}}=\dfrac{\sqrt{a}-\sqrt{b}}{a-b}$

7.

Rationalise denominator

$\dfrac{1}{\sqrt{a}-\sqrt{b}}=\dfrac{\sqrt{a}+\sqrt{b}}{a+b}$

8.

Lagrange's Identity

$\sqrt{a \pm \sqrt{b}}=\dfrac{\sqrt{a+\sqrt{a^2-b}}}{2} \pm \dfrac{\sqrt{a-\sqrt{a^2-b}}}{2}$

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