Question

rationalize the denominator of the following: 1/√5-√2

Answer 1

$\bf \huge \dag \: \: \: \: \frac{1}{ \sqrt{5} - \sqrt{2} } \\ \\ \\ \hookrightarrow \frac{1}{ \sqrt{5} - \sqrt{2} } \times \frac{ \sqrt{5} + \sqrt{2} }{ \sqrt{5} + \sqrt{2} } \\ \\ \hookrightarrow \frac{ \sqrt{5} + \sqrt{2} }{ {( \sqrt{5} )}^{2} - {( \sqrt{2} )}^{2} } \\ \\ \hookrightarrow \: \: \frac{ \sqrt{5} + \sqrt{2} }{5 - 2} \: \: = \frac{ \sqrt{5} + \sqrt{2} }{3}$

$<marquee>MARK BRAINLIEST ⤴⤴$

Answer 2

Hope this helps you ;)

$\frac{1}{ \sqrt{5} - \sqrt{2} }$

$= \frac{1}{ \sqrt{5} - \sqrt{2} } \times \frac{( \sqrt{5} + \sqrt{2}) }{( \sqrt{5} + \sqrt{2} )}$

$= \frac{ \sqrt{5} + \sqrt{2} }{ { \sqrt{5} }^{2} - { \sqrt{2} }^{2} }$

$= \frac{ \sqrt{5} + \sqrt{2} }{5 - 2}$

$= \frac{ \sqrt{5} + \sqrt{2} }{3}$