Question

Rationalise denominator = √7+√2 by √7-√2

Answer 1

Hi...☺

Here is your answer...✌
=================================

On rationalising ,
We get,

$\frac{ \sqrt{7} + \sqrt{2} }{ \sqrt{7} - \sqrt{2} } \times \frac{ \sqrt{7} + \sqrt{2} }{ \sqrt{7} + \sqrt{2} } \\ \\ = \frac{( { \sqrt{7} })^{2} + { (\sqrt{2}) }^{2} + 2 \sqrt{14} }{ ({ \sqrt{7} )}^{2} - {( \sqrt{2}) }^{2} } \\ \\ = \frac{7 + 2 + 2 \sqrt{14} }{7 - 2} \\ \\ = \frac{ 9 + 2 \sqrt{14} }{5}$

Answer 2

(root7 + root2)/(root7 - root2) × (root7 + root2)/(root7 + root2)

= (root7 + root2)^2 / (root7)^2 - (root2)^2

$( \sqrt{7} ) {}^{2} + ( \sqrt{2} ) {}^{2} + 2( \sqrt{7} )( \sqrt{2} ) \div 7 - 2$

$7 + 2 + 2 \sqrt{14} \div 5$

$9 + 2 \sqrt{14} \div 5 \: \: is \: answer$