Question

rationalize:-. fast , very fast​

Answer 1

$\sf{Answer}$

Given :-

$\dfrac{2}{ \sqrt{5} - \sqrt{6} }$

To do :-

Rationalize the denominator

Solution:-

For Rationalising the denominator we have to multiply with Rationalising factor

Rationalising factor is nothing but just we have to change the sign

$\sqrt{5} - \sqrt{6} = \sqrt{5} + \sqrt{6}$

This is the Rationalising factor

So, multiply and divide with its Rationalizing factor

$\dfrac{2}{ \sqrt{5} - \sqrt{6} } \times \dfrac{ \sqrt{5} + \sqrt{6} }{ \sqrt{5} + \sqrt{6} }$

$\dfrac{2( \sqrt{5} + \sqrt{6}) }{ \sqrt{5 - } \sqrt{6} \times \sqrt{5} + \sqrt{6} }$

$\dfrac{2 \sqrt{5 } + 2 \sqrt{6} }{ \sqrt(5) {}^{2} - \sqrt{(6)} {}^{2} }$

$\dfrac{2 \sqrt{5} + 2 \sqrt{6} }{5 - 6}$

$\dfrac{2 \sqrt{5} + 2 \sqrt{6} }{ - 1}$

$\dfrac{ - 2 \sqrt{5} + 2 \sqrt{6} }{1}$

$\dfrac{2 \sqrt{6} - 2 \sqrt{5} }{1}$

Hence denomiantor rationalised!

Formula used for Rationalising denominator

(a + b) ( a - b) = a²-b²

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