# Quotient theorem for square roots

#### Richay

##### New member
I got 3 out of the 4 problems on this right. Yet i'm still stuck on one.

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#### soroban

##### Elite Member
Hello, Richay!

$$\displaystyle \L -3\sqrt{\frac{2}{3}}\,+\,2\sqrt{\frac{3}{2}}$$

Simplify each term:

$$\displaystyle \L\;\;-3\cdot\sqrt{\frac{2}{3}\cdot\frac{3}{3}}\:=\:-3\cdot\sqrt{\frac{6}{9}}\:=\:-3\cdot\frac{\sqrt{6}}{\sqrt{9}} \:=\;-\not{3}\cdot\frac{\sqrt{6}}{\not{3}}\:=\:-\sqrt{6}$$

$$\displaystyle \L\;\;2\cdot\sqrt{\frac{3}{2}\cdot\frac{2}{2}}\:=\:2\cdot\sqrt{\frac{6}{4}}\:=\:2\cdot\frac{\sqrt{6}}{\sqrt{4}}\:=\:\not{2}\cdot\frac{\sqrt{6}}{\not{2}}\:=\;\sqrt{6}$$

The problem becomes: $$\displaystyle \L\,-\sqrt{6}\,+\,\sqrt{6}\:=\:0$$

#### Richay

##### New member
Hey.
Thanks for the explenation.
K i see how it's done