How do you rationalize the denominator and simplify $\sqrt{\frac{2}{3}}$ $sqrt(2/3)$ ?

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How do you rationalize the denominator and simplify $\sqrt{\frac{2}{3}}$ $sqrt(2/3)$ ?

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Answer 1 · 2016-05-09T12:45:30

$\frac{\sqrt{6}}{3}$ $sqrt(6)/3$

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'

$2 \times 1 = 2$ $2xx1=2$ and so on

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

Write as: $\frac{\sqrt{2}}{\sqrt{3}}$ $" "sqrt(2)/(sqrt(3))$

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

$\frac{\sqrt{2}}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}$ $" "sqrt(2)/(sqrt(3))xxsqrt(3)/(sqrt(3))$

$\frac{\sqrt{2} \times \sqrt{3}}{{(\sqrt{3})}^{2}}$ $" "(sqrt(2)xxsqrt(3))/(sqrt(3))^2$

$\frac{\sqrt{2 \times 3}}{3} = \frac{\sqrt{6}}{3}$ $sqrt(2xx3)/3 = sqrt(6)/3$

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How do you rationalize the denominator and simplify $\sqrt{\frac{2}{3}}$ $sqrt(2/3)$ ?

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