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Rational and Irrational Numbers — MATHEMATICS STD 9 — Question

ICSE BoardEnglish MediumSTD 9MATHEMATICSRational and Irrational Numbers2 Marks
Question
Simplify : $\frac{\sqrt{2}}{\sqrt{6}-\sqrt{2}}-\frac{\sqrt{3}}{\sqrt{6}+\sqrt{2}}$
✓

Answer

$ \frac{\sqrt{2}}{\sqrt{6}-\sqrt{2}}-\frac{\sqrt{3}}{\sqrt{6}+\sqrt{2}}$
$=\frac{\sqrt{2}}{\sqrt{6}-2}-\frac{\sqrt{3}}{\sqrt{6}+\sqrt{2}}$
$=\frac{\sqrt{2}(\sqrt{6}+\sqrt{2})-\sqrt{3}(\sqrt{6}-\sqrt{2})}{(\sqrt{6})^2-(\sqrt{2})^2}$
$ =\frac{\sqrt{12}+2-\sqrt{18}+\sqrt{6}}{6-2}$
$ =\frac{2 \sqrt{3}+2-3 \sqrt{2}+\sqrt{6}}{4}$

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