How do you simplify sqrt 2 / sqrt 10?

Aug 14, 2017

$\frac{\sqrt{5}}{5}$

Explanation:

$\text{to simplify a fraction with radicals we make the denominator}$
$\text{rational, that is remove the radical}$

$\text{using the "color(blue)"laws of radicals}$

•color(white)(x)sqrtaxxsqrta=a

•color(white)(x)sqrtaxxsqrtbhArrsqrtab

$\text{to remove the radical from the denominator multiply the}$
$\text{numerator and denominator by } \sqrt{10}$

$\frac{\sqrt{2}}{\sqrt{10}} \times \frac{\sqrt{10}}{\sqrt{10}}$

$= \frac{\sqrt{2 \times 10}}{10}$

$= \frac{\sqrt{20}}{10} = \frac{\sqrt{4 \times 5}}{10} = \frac{\sqrt{4} \times \sqrt{5}}{10} = \frac{2 \sqrt{5}}{10} = \frac{\sqrt{5}}{5}$