Question

Rationalize -: {1 /( √11 -√2)}

Answer 1

Step-by-step explanation:

$\frac{1}{ \sqrt{11} - \sqrt{2} } \times \frac{ \sqrt{11} + \sqrt{2} }{ \sqrt{11} + \sqrt{2} }$

$\frac{ \sqrt{11} + \sqrt{2} }{11 - 2}$

$\frac{ \sqrt{11} + \sqrt{2} }{9}$

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Answer 2

${\huge{\underline{\underline{\bf{\pink{Answer}}}}}}$

To Rationalize the denominator -

$\frac{1}{ \sqrt{11} - \sqrt{2} }$

Solution -

To , Rationalize , we Multiply the neumerator and the denominator by the conjugate of the denominator ,

here , it is (√11 + √2)

$\implies \: \frac{1}{ \sqrt{11} - \sqrt{2} } \times \frac \red{ \sqrt{11} + \sqrt{2} } \red{ \sqrt{11} + \sqrt{2} }$

we know , (a + b)(a - b) = a² - b²

$\implies \: \frac{ \sqrt{11} + \sqrt{2} }{ {( \sqrt{11} )}^{2} - {( \sqrt{2}) }^{2} }$

$\implies \: \frac{ \sqrt{11} + \sqrt{2} }{11 - 2} \\ \\ \implies \: \frac \green{ \sqrt{11} + \sqrt{2} } \green{9}$