Question

Rationalise the denominator √2/√2+√3-√5​

Answer 1

Answer:-

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

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

$⇒ \frac{2 + \sqrt{6} + \sqrt{10} }{2 + 3 + 2 \sqrt{6} - 5 }$

$⇒ \frac{2 + \sqrt{6} + \sqrt{10} }{2 + \sqrt{6} }$

$⇒ \frac{2 + \sqrt{6} + \sqrt{10} }{2 \sqrt{6} } \times \frac{ \sqrt{6} }{ \sqrt{6} }$

$⇒ \frac{2 \sqrt{6} + 6 + \sqrt{60} }{2 \times 6}$

$⇒ \frac{2( \sqrt{6} + 3 + \sqrt{15} }{2 \times 6}$

$⇒ \frac{3 + \sqrt{6} + \sqrt{15} }{6}$

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