Question

Rationalise the denominator of 1/√3 - √2​

Answer 1

Step-by-step explanation:

$\underline{\underline{\sf{➤ \:\: Solution }}}$

$\sf\: \: \: \dfrac{1}{ \sqrt{3} - \sqrt{2} }$

On rationalising,

$\sf \implies \dfrac{1}{ \sqrt{3} - \sqrt{2} } \times \dfrac{\sqrt{3} + \sqrt{2} }{\sqrt{3} + \sqrt{2} }$

Combine the fractions,

$\sf \implies \dfrac{1(\sqrt{3} + \sqrt{2}) }{(\sqrt{3} - \sqrt{2})(\sqrt{3} + \sqrt{2}) }$

We know that,

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

So,

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

$\sf \implies \dfrac{1(\sqrt{3} + \sqrt{2}) }{3 - 2 }$

$\sf \implies \dfrac{1(\sqrt{3} + \sqrt{2}) }{1 }$

$\sf \implies ( \sqrt{3} + \sqrt{2})$

Hence,

On rationalising we got,

$\implies \bf (\sqrt{3} + \sqrt{2})$