Rationalise the denominator of 1 2+3 - Vidyadip

Question

Rationalise the denominator of $\frac{1}{2+\sqrt{3}}$

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Answer

$\frac{1}{2+\sqrt{3}}=\frac{1}{2+\sqrt{3}} \times \frac{2-\sqrt{3}}{2-\sqrt{3}} \text { (Rationalise the denominator) }$
$=\frac{2-\sqrt{3}}{4-3}\left[\text { using } \mathrm{a}^2-\mathrm{b}^2=(\mathrm{a}+\mathrm{b})(\mathrm{a}-\mathrm{b})\right]$
$=2-\sqrt{3}$

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