Question

Simplify by rationalising the denominator
✓3+✓2 by ✓3-✓2 - ✓3-✓2 by ✓3+✓2​

Answer 1

$\mathfrak{\huge{Answer:-}} \\ \bold{\frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2} } - \frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} + \sqrt{2} } } \\ = \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2} } \times \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} + \sqrt{2} } - \frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} + \sqrt{2} } \times \frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} - \sqrt{2} } \\ = \frac{( \sqrt{3} + \sqrt{2} )( \sqrt{3} + \sqrt{2} ) }{( \sqrt{3} - \sqrt{2})( \sqrt{3} + \sqrt{2}) } - \frac{( \sqrt{3} - \sqrt{2})( \sqrt{3} + \sqrt{2})}{( \sqrt{3} + \sqrt{2} )( \sqrt{3} - \sqrt{2}) } \\ = \frac{ {( \sqrt{3} + \sqrt{2}) }^{2} }{ {( \sqrt{3} )}^{2} - {( \sqrt{2} )}^{2} } - \frac{ {( \sqrt{3} - \sqrt{2} )}^{2} }{ {( \sqrt{3} )}^{2} - {( \sqrt{2}) }^{2} } \\ = \frac{3 + 2 + 2 \sqrt{6} }{3 - 2} - \frac{3 + 2 - 2 \sqrt{6} }{3 - 2} \\ = \frac{5 + 2 \sqrt{6} }{1} - \frac{5 - 2 \sqrt{6} }{1} \\ = (5 + 2 \sqrt{6} ) - (5 - 2 \sqrt{6} ) \\ = 5 + 2 \sqrt{6} - 5 + 2 \sqrt{6} \\ = 5 - 5 + 2 \sqrt{6} + 2 \sqrt{6} \\ = 4 \sqrt{6} \\ \boxed{\boxed{\large{\bold{ \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2}} - \frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} + \sqrt{2} } = 4 \sqrt{6} }}}}$