Part 18 - Rationalisation I | Maths Made Easy

# Surds GCSE Maths Revision

## Part 18 – Rationalisation I

The previous examples are all correct, but in maths no fraction is left to have a surd in the denominator. Hence we need to ‘rationalise’ it. This uses the formula m/(n√a)×(n√a)/(n√a)=(mn√a)/(n2 a) .

This is done as follows:

Example:

Rationalise 2/(2√3)

Worked Solution:

Use the formula m/(n√a)×(n√a)/(n√a)=(mn√a)/(n2 a)

2/(2√3)×(2√3)/(2√3)=(2×2 \×√3)/(2×√3×2×√3)=(4√3)/(4×3)=(4√3)/12

Simplify numerator and denominator by 4 as they have a common factor (for more information please refer to the “HCF and LCM” tutorial). Hence,

(4√3)/12=√3/3

Rationalise $\frac{21}{3\sqrt{5}}$

Your answer can be written in the from $\frac{21\sqrt{3}}{b}$

Find the value of b.