Question

Rationalise the denominator:

√3 +√2/√3 -√2

[Answer: 5+2√6]​

Answer 1

Required Answer:-

Given To Rationalise:

• $\tt \dfrac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2}}$

Solution:

Given,

$\tt = \dfrac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2}}$

Multiplying numerator and denominator by (√3 + √2), we get,

$\tt = \dfrac{ (\sqrt{3} + \sqrt{2})( \sqrt{3} + \sqrt{2} )}{(\sqrt{3} - \sqrt{2})( \sqrt{3} + \sqrt{2})}$

Using identity a² - b² = (a + b)(a - b), we get,

$\tt = \dfrac{ (\sqrt{3} + \sqrt{2})( \sqrt{3} + \sqrt{2} )}{(\sqrt{3})^{2} - (\sqrt{2})^{2} }$

$\tt = \dfrac{ (\sqrt{3} + \sqrt{2})( \sqrt{3} + \sqrt{2} )}{3 - 2}$

$\tt = \dfrac{ (\sqrt{3} + \sqrt{2})( \sqrt{3} + \sqrt{2} )}{1}$

$\tt = (\sqrt{3} + \sqrt{2})( \sqrt{3} + \sqrt{2} )$

$\tt = (\sqrt{3} + \sqrt{2})^{2}$

Using identity (a + b)² = a² + 2ab + b², we get,

$\tt = (\sqrt{3})^{2} + (\sqrt{2})^{2} + 2 \times \sqrt{3 \times 2}$

$\tt =3 + 2+ 2\sqrt{6}$

$\tt =5 + 2\sqrt{6}$

★ Therefore, result obtained after rationalisation is - 5 + 2√6.

Answer:

• 5 + 2√6