Question

Rationalise the denominator
$\boxed{ \tt \: \dfrac{8}{ \sqrt{6} - 2}}$
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Answer 1

Answer:- 8 root 6 + 8


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Answer 2

Question :-

Rationalise the denominator

$\boxed{ \tt \: \dfrac{8}{ \sqrt{6} - 2}}$

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Solution :-

Given Information :-

$\sf \: \dfrac{8}{ \sqrt{6} - 2}$

To Find :-

Rationalise the denominator.

Calculation :-

$: \implies \frac{8}{ \sqrt{6} - 2} \times \frac{ \sqrt{6 + 2} }{ \sqrt{6 + 2} }$

$: \implies \frac{8( \sqrt{6 + 2} }{ ({ \sqrt{6}) }^{2} - {(2)}^{2} }$

$: \implies \frac{8 \sqrt{6} + 16}{6 - 4}$

$: \implies \frac{8 \sqrt{6} + 16 }{2}$

Cancelling 2 in denominator and 16 in numerator, We get,

$: \implies \frac{ 8\sqrt{6} + \cancel{ 16}}{ \cancel{2} }$

On cancelling, We get 8 in numerator,

$: \implies 8 \sqrt{6} + 8$

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Final Answer :-

$: \red\maltese \: \: \: \boxed{ 8 \sqrt{6} + 8}$

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