## Breaking Down Square Roots of Large Numbers

Break the number into its factors and multiply the square roots of those.
$\sqrt[2]{20} = \sqrt[2]{4 \times 5} = 2\sqrt[2]{5}$

## Fractions

General rule: $\sqrt[2]{\frac a b} = \frac{\sqrt[2]{a}}{\sqrt[2]{b}}$

e.g. $\sqrt[2]{\frac{9}{10}} = \frac{\sqrt[2]{9}}{\sqrt[2]{10}} = \frac{3}{\sqrt[2]{10}}$

However solutions never contain square roots in a denominator. Therefore the denominator has to be rationalized. Since $\frac{\sqrt[2]{10}}{\sqrt[2]{10}} = 1$, this process is as simple as multiplying the result with a fraction that contains its denominator on both sides:

$\frac{3}{\sqrt[2]{10}} \times \frac{\sqrt[2]{10}}{\sqrt[2]{10}} = \frac{3\sqrt[2]{10}}{10}$

This works in general because $\sqrt[2]{x} \times \sqrt[2]{x} = x$

Also fractions should be simplified where possible e.g. $\sqrt[2]{\frac{40}{2}} = \sqrt[2]{20}$

### Square Root Term in Polynomial Denominator

Given a fraction such as $\frac {2}{\sqrt{2}-1}$, forming a difference of squares gets rid of the root in the denominator:

$a^2-b^2=(a+b)(a-b)$

So

$\frac {2(\sqrt{2}+1)}{2-1}$

## Misc Notes

$\sqrt[2]{x^2} = x$