Question

Rationalize the denomenatar of 1 by root 5 minus root 2

Answer 1

Hey Pretty Stranger!

To Rationalize :

$\sf \: \dfrac{1}{ \sqrt{5} - \sqrt{2} }$

Multiply the numerator and denominator by the rationalisation factor of denominator :

$\longrightarrow \sf \: \dfrac{1 \times \sqrt{5 } + \sqrt{2} }{ \sqrt{5} - \sqrt{2} \times \sqrt{5} + \sqrt{2} }$

$\longrightarrow \sf \: \dfrac{ \sqrt{5} + \sqrt{2} }{( \sqrt{5}) ^{2} - ( \sqrt{2} ) ^{2} }$

[Used the algebraic identity (a -b) (a + b) = a² - b²]

$\longrightarrow \sf \: \dfrac{ \sqrt{5} + \sqrt{2} }{5 - 2 }$

$\longrightarrow \sf \: \dfrac{ \sqrt{5} + \sqrt{2} }{3}$

Hence, Denominator is rationalised.

Ab muskura do xD