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

Mar 22, 2018

$\sqrt{\frac{3}{2}} + \sqrt{\frac{2}{3}} = 5 \cdot \frac{\sqrt{6}}{6}$

#### Explanation:

$\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$
$\sqrt{\frac{3}{2}} + \sqrt{\frac{2}{3}} = \frac{\sqrt{3}}{\sqrt{2}} + \frac{\sqrt{2}}{\sqrt{3}}$
$\frac{a}{b} + \frac{c}{d} = \frac{a \cdot d + c \cdot b}{b \cdot d}$
$\sqrt{\frac{3}{2}} + \sqrt{\frac{2}{3}} = \frac{3 + 2}{\sqrt{6}}$
$\sqrt{\frac{3}{2}} + \sqrt{\frac{2}{3}} = \frac{5}{\sqrt{6}}$
$\sqrt{\frac{3}{2}} + \sqrt{\frac{2}{3}} = 5 \cdot \frac{\sqrt{6}}{6}$