Question

Rationalise the denominator in the following and hence evaluate by taking ${\displaystyle \sqrt{2}=1.414,\sqrt{3}=1.732}$ and ${\displaystyle \sqrt{5}=2.236}$, upto three places of decimal.

${\displaystyle \frac{\sqrt{10}-\sqrt{5}}{2}}$

Answer 1

Let ${\displaystyle E=\frac{\sqrt{10}-\sqrt{5}}{2}}$

= ${\displaystyle \frac{\sqrt{5}\sqrt{2}-\sqrt{5}}{2}}$

= ${\displaystyle \frac{\sqrt{5}(\sqrt{2}-1)}{2}}$  ...${\displaystyle [\because \sqrt{10}=\sqrt{2}\sqrt{5}]}$

= ${\displaystyle \frac{2.236(1.414-1)}{2}}$

= 1.118 × 0.414

= 0.46285 ≅ 0.463