Surds: GCSE Maths revision
A surd is a root that does not simplify to an integer, like √2. Keep it exact unless the question asks for a decimal.
Simplifying
Simplify √50
Rationalising the denominator
Multiply numerator and denominator by the surd on the bottom so the denominator becomes an integer.
1 / √3
Try these questions
Cover the answers and have a go first. Worked solutions are underneath.
Simplify √18
Simplify √72
Expand (√3 + 1)(√3 − 1)
Rationalise 5 / √5
Common mistakes
- Taking √(a + b) as √a + √b — that is false.
- Forgetting to multiply the numerator when rationalising.
Answers and working
Frequently asked questions
Is √4 a surd?
No. √4 = 2, which is rational. Surds stay irrational.
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