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Number systems — MATHS STD 9 — Question

Rajasthan BoardEnglish MediumSTD 9MATHSNumber systems1 Mark
Question
Rationalize the denominator of $\frac{1}{{\sqrt 5 + \sqrt 2 }}$
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Answer

$\frac{1}{{\sqrt 5 + \sqrt 2 }}$
multiply denominator and numerator by $\frac{1}{{\sqrt 5 - \sqrt 2 }}$
$=\frac{1}{\sqrt{5}+\sqrt{2}} \times \frac{\sqrt{5}-\sqrt{2}}{\sqrt{5}-\sqrt{2}}$
$=\frac{\sqrt{5}-\sqrt{2}}{(\sqrt{5})^{2}-(\sqrt{2})^{2}}=\frac{\sqrt{5}-\sqrt{2}}{5-2}$
$=\frac{\sqrt{5}-\sqrt{2}}{3}$

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