Question

Rationalize the denominator 4÷√11-√7​

Answer 1

Answer:

$= > \sqrt{11} + \sqrt{7}$

Step-by-step explanation:

$\frac{4}{ \sqrt{11} - \sqrt{7} }$

$Since, \: the \: denominator \: \\ = \sqrt{11} - \sqrt{7}$

$It's \: rationalizing \: factor \\ = \sqrt{11} + \sqrt{7}$

$Therefore \: \frac{4}{ \sqrt{11} - \sqrt{7} } = \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \frac{4}{ \sqrt{11} - \sqrt{7} } \times \frac{ \sqrt{11} + \sqrt{7} }{ \sqrt{11} + \sqrt{7} }$

$= \frac{4( \sqrt{11} + \sqrt{7} )}{( \sqrt{11} ){}^{2} -( \sqrt{7} ) {}^{2} } = \frac{4( \sqrt{11 } + \sqrt{7} )}{11 - 7}$

$= \frac{4( \sqrt{11} + \sqrt{7}) }{4} = > \sqrt{11} + \sqrt{7}$