Rationalising simple denominators

Text

Rationalise the denominator:

• (a) $\dfrac{6}{\sqrt{3}}$
• (b) $\dfrac{10}{2\sqrt{5}}$

Solution

(a) $\dfrac{6}{\sqrt3}\cdot\dfrac{\sqrt3}{\sqrt3}=\dfrac{6\sqrt3}{3}=2\sqrt3$. (b) $\dfrac{10}{2\sqrt5}=\dfrac{5}{\sqrt5}=\dfrac{5\sqrt5}{5}=\sqrt5$.

$\boxed{\;(a)\;2\sqrt{3}\qquad (b)\;\sqrt{5}\;}$