Question

Rationalize the denominator =1/√5 + √2​

Answer 1

$= = > \: \: \frac{1}{ \sqrt{5} + \sqrt{2} } \\ \\ = = > \: \: \frac{1}{ \sqrt{5} + \sqrt{2} } \times \frac{ \sqrt{5} - \sqrt{2} }{ \sqrt{5} - \sqrt{2} } \\ \\ = = > \: \: \frac{ \sqrt{5} - \sqrt{2} }{ {( \sqrt{5} )}^{2} - {( \sqrt{2}) }^{2} } \\ \\ = = > \: \: \frac{ \sqrt{5} - \sqrt{2} }{5 - 2} \\ \\ = = > \: \: \frac{ \sqrt{5} - \sqrt{2} }{3}$

Answer 2

Answer:

$\frac{1}{ \sqrt{5} + \sqrt{2} } \\ multiply \: by \: \frac{ \sqrt{5} - \sqrt{2} }{ \sqrt{5} - \sqrt{2} } \\ = ( \frac{1}{ \sqrt{5} + \sqrt{2} } )( \frac{ \sqrt{5} - \sqrt{2} }{ \sqrt{5} - \sqrt{2} } ) \\ apply \: formula \: (x + y) (x - y) = {x}^{2} - {y}^{2} \\ = \frac{ \sqrt{5} - \sqrt{2} }{( \sqrt{5} ) {}^{2} - ( \sqrt{2}) {}^{2} } \\ = \frac{ \sqrt{5} - \sqrt{2} }{5 - 2} \\ = \frac{ \sqrt{5} - \sqrt{2} }{3} \: \: ans \\ hint : ( \sqrt{n} ) {}^{2} = n$