Rationalize the denominator:
$\frac{1}{2\ +\ \sqrt{3}}$>

Given: $\frac{1}{2\ +\ \sqrt{3}}$

To do: Here we have to rationalize the denominator of the given expression $\frac{1}{2\ +\ \sqrt{3}}$.

Solution:

$\frac{1}{2\ +\ \sqrt{3}}$

Multiplying and dividing it with $2\ -\ \sqrt{3}$

$=\ \frac{1}{2\ +\ \sqrt{3}} \ \times \ \frac{2\ -\ \sqrt{3}}{2\ -\ \sqrt{3}}$

$=\ \frac{2\ -\ \sqrt{3}}{( 2)^{2} \ -\ \left(\sqrt{3}\right)^{2}}$

$=\ \frac{2\ -\ \sqrt{3}}{4\ -\ 3}$

$=\ \frac{2\ -\ \sqrt{3}}{1}$

$=\ \mathbf{2\ -\ \sqrt{3}}$

So, the answer is $2\ -\ \sqrt{3}$.

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Updated on: 10-Oct-2022

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