Question
Rationalise the denominators of : $\frac{3}{\sqrt{5}+\sqrt{2}}$
✓
Answer
$ \frac{3}{\sqrt{5}+\sqrt{2}} \times\left(\frac{\sqrt{5}-\sqrt{2}}{\sqrt{5}-\sqrt{2}}\right)$
$= \frac{3(\sqrt{5}-\sqrt{2})}{(\sqrt{5})^2-(\sqrt{2})^2}$
$= \frac{3(\sqrt{5}-\sqrt{2})}{5-2}$
$= \sqrt{5}-\sqrt{2}$
$= \frac{3(\sqrt{5}-\sqrt{2})}{(\sqrt{5})^2-(\sqrt{2})^2}$
$= \frac{3(\sqrt{5}-\sqrt{2})}{5-2}$
$= \sqrt{5}-\sqrt{2}$
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