# How do you simplify square root of 70 / square root of 40?

Sep 19, 2015

$\frac{\sqrt{70}}{\sqrt{40}} = \frac{\sqrt{7}}{2}$

#### Explanation:

Using prime factorization, $\frac{\sqrt{70}}{\sqrt{40}}$ can be rewritten as sqrt(7*5*2) / sqrt(5*2^3

$\sqrt{5 \cdot 2}$ is found in both the numerator and denominator and cancel each other out:

$\frac{\sqrt{7 \cdot 5 \cdot 2}}{\sqrt{5 \cdot {2}^{3}}} = \frac{\sqrt{7}}{\sqrt{{2}^{2}}}$

The denominator $\sqrt{{2}^{2}}$, or $\sqrt{4}$, is a perfect square which simplifies to $2$:

$\frac{\sqrt{7}}{\sqrt{{2}^{2}}} = \frac{\sqrt{7}}{2}$

This is the simplified expression.