Rationalise the denominator of 1 2+3 - Vidyadip

Question

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

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Answer

$\frac{1}{2+\sqrt{3}}$ = $\frac{1}{2+\sqrt{3}} \times \frac{2-\sqrt{3}}{2-\sqrt{3}}$ (Rationalise the denominator)

$=\frac{2-\sqrt{3}}{4-3}$ [using a² - b²= (a+b)(a-b)]

$=2-\sqrt{3}$

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