# What is Square root of 2/3 + square root of 3/2?

Jun 15, 2015

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

Split the fractions:
$= \frac{\sqrt{2}}{\sqrt{3}} + \frac{\sqrt{3}}{\sqrt{2}}$

Cross-multiply:
$= \frac{\sqrt{2}}{\sqrt{3}} \cdot \frac{\sqrt{2}}{\sqrt{2}} + \frac{\sqrt{3}}{\sqrt{2}} \cdot \frac{\sqrt{3}}{\sqrt{3}}$

$= \frac{2}{\sqrt{6}} + \frac{3}{\sqrt{6}}$

$= \frac{5}{\sqrt{6}}$

Get rid of the radical in the denominator:
$= \frac{5}{\sqrt{6}} \cdot \frac{\sqrt{6}}{\sqrt{6}}$

Simplify:
$= \frac{5 \sqrt{6}}{6}$