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Irrational Numbers — MATHEMATICS STD 9 — Question

ICSE BoardEnglish MediumSTD 9MATHEMATICSIrrational Numbers5 Marks
Question
Simplify by rationalising the denominator in the following.$\frac{\sqrt{7}-\sqrt{5}}{\sqrt{7}+\sqrt{5}}$
✓

Answer

$\frac{\sqrt{7}-\sqrt{5}}{\sqrt{7}+\sqrt{5}} $
$=\frac{\sqrt{7}-\sqrt{5}}{\sqrt{7}+\sqrt{5}} \times \frac{\sqrt{7}-\sqrt{5}}{\sqrt{7}-\sqrt{5}} $
$ =\frac{(\sqrt{7}-\sqrt{5})^2}{(\sqrt{7})^2-(\sqrt{5})^2} $
$=\frac{7+5-2 \sqrt{35}}{7-5} $
$=\frac{12-2 \sqrt{35}}{2} $
$=6-\sqrt{35}$

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