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:


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,


Your turn:

Rationalise \frac{21}{3\sqrt{5}}

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

Find the value of b.

Enter your answer here:

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