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Number systems — MATHS STD 9 — Question

Rajasthan BoardEnglish MediumSTD 9MATHSNumber systems1 Mark
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 $a^2 - b^{2 }= (a+b)(a-b)]$
$=2-\sqrt{3}$

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