Question

Rationalise the denominator 1/5√2​

Answer 1

Step-by-step explanation:

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Answer 2

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In the given question

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

$\sf \colorbox{skyblue} {On Rationalising The Number}$

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

$\sf \colorbox{lightgreen} {On Applying}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: (a + b)(a - b) = {a}^{2} - {b}^{2}$

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

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

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

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