Question

(7) Rationalize the denominator in the following
(1). 1/√7-√6
(2). 1/√5+√2​

Answer 1

$❶ \frac{1}{ \sqrt{7} - \sqrt{6} }$

$⇢ \frac{1}{ \sqrt{7} - \sqrt{6} } \times \frac{ \sqrt{7} + \sqrt{6} }{ \sqrt{7 + \sqrt{6} } }$

$⇢ \frac{ \sqrt{7} + \sqrt{6} }{ {( \sqrt{7}) }^{2} -{( \sqrt{6} })^{2} }$

$⇢ \sqrt{7} + \sqrt{6}$

Hence, Rationalised

$➋ \frac{1}{ \sqrt{5} + \sqrt{2} }$

$⇢ \frac{1}{ \sqrt{5} - \sqrt{2} } \times \frac{ \sqrt{5} + \sqrt{2} }{ \sqrt{5} + \sqrt{2} }$

$⇢ \frac{ \sqrt{5} + \sqrt{2} }{ {( \sqrt{5} )}^{2} - {( \sqrt{2} })^{2} }$

$⇢ \frac{ \sqrt{5} + \sqrt{2} }{3}$

Hence ,Rationalised