Question

Simplify:—
$\frac{2}{ \sqrt{5} - \sqrt{3} - \sqrt{2} }$
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Answer 1

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Simplify :—

$\frac{2}{ \sqrt{5} - \sqrt{3} - \sqrt{2} }$

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$⇒ \frac{2}{ (\sqrt{5} - \sqrt{3}) - \sqrt{2} } \times \frac{(\sqrt{5} - \sqrt{3}) + \sqrt{2}}{(\sqrt{5} - \sqrt{3}) + \sqrt{2}}$

$⇒ \frac{2 \sqrt{5} - 2 \sqrt{3} + 2 \sqrt{2} }{5 + 3 - 2 \sqrt{15} - 2}$

$⇒ \frac{ \cancel2 \sqrt{5} - \cancel2 \sqrt{3} + \cancel2 \sqrt{2} }{ \cancel6 - \cancel2 \sqrt{15} }$

$⇒ \frac{ \sqrt{5} - \sqrt{3} + \sqrt{2} }{3 - \sqrt{15} }$

$⇒ \frac{ \sqrt{5} - \sqrt{3} + \sqrt{2} }{3 - \sqrt{15} } \times \frac{3 + \sqrt{15} }{3 + \sqrt{15} }$

$⇒ - \frac{1}{6} ( \cancel{3 \sqrt{5}} + 5 \sqrt{3} - 3 \sqrt{3} \cancel{- 3 \sqrt{5}} + 3 \sqrt{2} + \sqrt{30} )$

$⇒ - ( \frac{2 \sqrt{3} + 3 \sqrt{2} + \sqrt{30} }{6} )$

Answer 2

Answer:

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