Question

Rationalise the denominator and simplify $\frac{1}{2}\sqrt{\frac{2a}{5}}$

Answer 1

We rationalise the denominator of $\frac{\sqrt{2a}}{2\sqrt{5}}$ by multiplying $\sqrt{5}$ in the numerator and denominator as follows:

$\frac{\sqrt{2a}}{2\sqrt{5}}\times \frac{\sqrt{5}}{\sqrt{5}}=\frac{\sqrt{10a}}{2\sqrt{25}}=\frac{\sqrt{10a}}{2\times 5}=\frac{\sqrt{10a}}{10}$

Hence, $\frac{\sqrt{2a}}{2\sqrt{5}}=\frac{\sqrt{10a}}{10}$