Question

Rationalise the denominator of 1/root 11 + root 7

Answer 1

Step-by-step explanation:

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Answer 2

$\displaystyle \sf{ \frac{1}{ \sqrt{11} + \sqrt{7} } } = \frac{ \sqrt{11} - \sqrt{7} }{4}$

Given :

$\displaystyle \sf{ \frac{1}{ \sqrt{11} + \sqrt{7} } }$

To find :

To rationalize the denominator

Solution :

Step 1 of 2 :

Write down the given expression

Here the given expression is

$\displaystyle \sf{ \frac{1}{ \sqrt{11} + \sqrt{7} } }$

Step 2 of 2 :

Rationalize the denominator

$\displaystyle \sf{ \frac{1}{ \sqrt{11} + \sqrt{7} } }$

Multiplying both of the numerator and denominator by √11 - √7 we get

$\displaystyle \sf{ \frac{1}{ \sqrt{11} + \sqrt{7} } }$

$\displaystyle \sf{ = \frac{(\sqrt{11} - \sqrt{7})}{ (\sqrt{11} + \sqrt{7})(\sqrt{11} - \sqrt{7}) } }$

$\displaystyle \sf{ = \frac{(\sqrt{11} - \sqrt{7})}{ {(\sqrt{11} )}^{2} - { ( \sqrt{7}) }^{2} } }$

$\displaystyle \sf{ = \frac{(\sqrt{11} - \sqrt{7})}{ 11 - 7 } }$

$\displaystyle \sf{ = \frac{\sqrt{11} - \sqrt{7}}{ 4 } }$

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