Question

rationalise the denominator of

$\frac{1}{ \sqrt{5 } + \sqrt{2} }$
​

Answer 1

Given :

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

To find :

Rationalise given number

Identity used :

• (a+b)(a-b) = a² - b²

Steps to follow :

For rationalization of denominator { given in form of (a+b) }

• Multiply and divide the number by (a-b):

Solution :

$\sf \implies \: \dfrac{1}{ \sqrt{5} + \sqrt{2} } \times \dfrac{ \sqrt{5} - \sqrt{2} }{ \sqrt{5} - \sqrt{2} } \\ \\ \sf \implies \: \dfrac{ \sqrt{5} - \sqrt{2} }{ { (\sqrt{5} )}^{2} - {( \sqrt{2} )}^{2} } \\ \\ \sf \implies \: \dfrac{ \sqrt{5} - \sqrt{2} }{5 - 2} \\ \\ \sf \implies \: \dfrac{ \sqrt{5} - \sqrt{2} }{3}$

ANSWER :

$\sf \bold{ \dfrac{ \sqrt{5} - \sqrt{2} }{3} }$