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boitshupoO

Answered question

2021-08-15

To calculate: The simplified form of the expression ,

\frac{12}{\sqrt{6} + \sqrt{2}}

Bertha Stark

Skilled2021-08-16Added 96 answers

The solution is written below

2021-12-24

Step

$\frac{12}{\sqrt{6} - \sqrt{2}} = \frac{12}{\sqrt{6} - \sqrt{2}} \times \frac{\sqrt{6} + \sqrt{2}}{\sqrt{6} + \sqrt{2}}$

$= \frac{12 (\sqrt{6} + \sqrt{2})}{(\sqrt{6})^{2} - (\sqrt{2})^{2}}$

$= \frac{12 (\sqrt{6} + \sqrt{2})}{6 - 2}$

$= \frac{12 (\sqrt{6} + \sqrt{2})}{4}$

Simplifying further,

$\frac{12}{\sqrt{6} - \sqrt{2}} = 3 (\sqrt{6} + \sqrt{2})$

Hence,the simplification of the given expression is $3 (\sqrt{6} + \sqrt{2})$

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