# How do you rationalize the denominator and simplify sqrt(2/3)?

May 9, 2016

$\frac{\sqrt{6}}{3}$

#### Explanation:

It is mathematically frowned up to have a root in the denominator. So it is better to 'get rid' of it if you can.

This is done using the following 'trick'!

If you multiply a value by 1 you do not change its 'worth'

$2 \times 1 = 2$ and so on

The value 1 can be written in many forms: 4-3; 0+2; 2/2 ; sqrt(3)/sqrt(3)
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Given$\text{ } \sqrt{\frac{2}{3}}$

Write as:$\text{ } \frac{\sqrt{2}}{\sqrt{3}}$

Multiply by 1 but in the form of $1 = \frac{\sqrt{3}}{\sqrt{3}}$ giving

$\text{ } \frac{\sqrt{2}}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}$

$\text{ } \frac{\sqrt{2} \times \sqrt{3}}{\sqrt{3}} ^ 2$

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