Question

rationalize the denominator in the following
$\frac{1}{ \sqrt{5 } + \sqrt{2} }$
​

Answer 1

$\mathtt{\huge{\underline{\red{Answer\: :}}}}$

☞ 1 / √5 + √2

=> 1 / ( 25 + 4 )

=> 1 / 29

= > 0.03

Answer 2

Solution:-

${ \tt{\dashrightarrow{\huge{ \frac{1}{ \sqrt{5} + \sqrt{2} } }}}}$

For rationalization we need to take conjugate pair of denominator

√5 + √2 is √5 - √2

${ \tt{\dashrightarrow{\huge{ \frac{1}{ \sqrt{5} + \sqrt{2} } \times \frac{ \sqrt{5} - \sqrt{2} }{ \sqrt{5} - \sqrt{2} } }}}}$

${ \tt{\dashrightarrow{\huge{ \frac{ \sqrt{5} - \sqrt{2} }{ \sqrt{5} + \sqrt{2} \times (\sqrt{5} - \sqrt{2} ) } }}}}$

${ \tt{\dashrightarrow{\huge{ \frac{ \sqrt{5} - \sqrt{2} }{ \sqrt{5 \times 5 } - \sqrt{2 \times 2} } }}}}$

${ \tt{\dashrightarrow{\huge{ \frac{ \sqrt{5} - \sqrt{2} }{ \sqrt{25} - \sqrt{4} } }}}}$

${ \tt{\dashrightarrow{\huge{ \frac{ \sqrt{5} - \sqrt{2} }{5 - 2} }}}}$

${ \tt{\dashrightarrow{\huge{ \frac{ \sqrt{5} - \sqrt{2} }{3} }}}}$

i hope it helps you.