# How do you simplify sqrt5/sqrt15?

Apr 21, 2016

$\frac{\sqrt{3}}{3}$

#### Explanation:

Multiply a number by 1 and its inherent value does not change. Multiply by 1 but in an equivalent form and you do not change its value but you do change the way it looks.

Given:$\text{ } \frac{\sqrt{5}}{\sqrt{15}}$

Multiply by 1 but in the form $1 = \frac{\sqrt{15}}{\sqrt{15}}$ giving

$\frac{\sqrt{5} \sqrt{15}}{\sqrt{15} \sqrt{15}}$

$\frac{\sqrt{5} \sqrt{15}}{15}$

$\frac{\sqrt{5 \times 15}}{15}$

$\frac{\sqrt{5 \times 5 \times 3}}{15}$

$\frac{5 \sqrt{3}}{15}$

$\frac{\sqrt{3}}{3}$

Apr 21, 2016

$\frac{\sqrt{5}}{\sqrt{15}} = \frac{\sqrt{3}}{3}$

#### Explanation:

(sqrt5)/(sqrt15)=cancel(sqrt5)/(cancel(sqrt5)*sqrt3)=1/sqrt3=sqrt3/(sqrt3*sqrt3)=sqrt3/(sqrt3)^²=sqrt3/3