Question
Simplify by rationalising the denominator in the following.$\frac{5}{\sqrt{7}-\sqrt{2}}$
✓
Answer
$ \frac{5}{\sqrt{7}-\sqrt{2}}$
$= \frac{5}{\sqrt{7}-\sqrt{2}} \times \frac{\sqrt{7}+\sqrt{2}}{\sqrt{7}+\sqrt{2}}$
$= \frac{5(\sqrt{7}+\sqrt{2})}{(\sqrt{7})^2+(\sqrt{2})^2}$
$= \frac{5(\sqrt{7}+\sqrt{2})}{7-2}$
$= \frac{5(\sqrt{7}+\sqrt{2})}{5}$
$= \sqrt{7}+\sqrt{2}$
$= \frac{5}{\sqrt{7}-\sqrt{2}} \times \frac{\sqrt{7}+\sqrt{2}}{\sqrt{7}+\sqrt{2}}$
$= \frac{5(\sqrt{7}+\sqrt{2})}{(\sqrt{7})^2+(\sqrt{2})^2}$
$= \frac{5(\sqrt{7}+\sqrt{2})}{7-2}$
$= \frac{5(\sqrt{7}+\sqrt{2})}{5}$
$= \sqrt{7}+\sqrt{2}$
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