# What is the square root of the square root of 32/72?

Jun 13, 2018

$= \frac{\sqrt{6}}{3} \approx 0.816$

#### Explanation:

$= \sqrt{\sqrt{\frac{32}{72}}}$

$= \sqrt{\sqrt{\frac{4}{9}}}$

$= \frac{\sqrt{\sqrt{4}}}{\sqrt{\sqrt{9}}}$

$= \frac{\sqrt{2}}{\sqrt{3}}$

rationalize the denominator:

$= \frac{\sqrt{2}}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}}$

$= \frac{\sqrt{6}}{3} \approx 0.816$