Number (Higher) · Higher
Surds
Simplifying surds, expanding brackets with surds, and rationalising the denominator.
A surd is an irrational root (e.g. √2, √3) left in exact form. Higher tier expects confident simplification and rationalising.
Practice lesson for the WJEC Mathematics and Numeracy Double Award. This is not an official WJEC page.
Simplifying surds
√(ab) = √a × √b
√(a/b) = √a / √b
Pull out square factors:
√12 = √(4×3) = 2√3
√50 = √(25×2) = 5√2
Worked example
Simplify √72.
Solution
√72 = √(36×2) = **6√2**
Rationalising the denominator
Multiply numerator and denominator by the surd in the denominator:
1/√5 = √5 / 5
For two terms: multiply by the conjugate.
1/(√5 − 2) → multiply by (√5 + 2)
Worked example
Rationalise 3/√7.
Solution
3/√7 × √7/√7 = **3√7 / 7**
Practice questions
Try these without looking at the answers first.
Q1.Simplify √18.
Show answer
3√2
Q2.Rationalise 1/√3.
Show answer
√3 / 3
Q3.Simplify √8 + √2.
Hint: √8 = 2√2
Show answer
3√2