Surds
Irrational square roots: √2, √3, √5. Simplify and rationalise denominators. Higher tier.
A surd is a square root that doesn't simplify to a whole number. Higher tier requires simplification (√50 = 5√2), addition (only of like surds), and rationalising denominators (multiplying by √a/√a).
Worked examples
√50 = √25 × √2 = 5√2.
3√2 + 4√2 = 7√2. Like surds add as terms.
1/√3 = (1 × √3) / (√3 × √3) = √3/3. Denominator rationalised.
Frequently asked questions
Why rationalise?
Convention; some calculations need a rational denominator (e.g. summing fractions). Also a marked GCSE skill.
Conjugate pairs?
(a + √b)(a − √b) = a² − b is rational. Used to rationalise denominators with surds in.