Question

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

Answer 1

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

$\frac{\sqrt{5}}{\sqrt{2y}}\times \frac{\sqrt{2y}}{\sqrt{2y}}=\frac{\sqrt{10y}}{\sqrt{4y^2}}=\frac{\sqrt{10y}}{2y}$

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