Simplifying surds practice questions

To simplify a surd, find the largest square factor of the number under the root, split the root, and take the square root of the square factor outside. For example, the square root of 12 becomes the square root of 4 times 3, which simplifies to 2 root 3.

A surd is a root that cannot be simplified to a whole number, such as √12. Leaving answers in surd form keeps them exact, which is why GCSE Higher and A-level both demand it.

The method, step by step

1. Look for a square factor. Find the largest square number that divides into the value under the root.
2. Split the root. √(a × b) can be written as √a × √b.
3. Take the square root out. The square number becomes a whole number in front.
4. Add like surds only. 3√2 + 4√2 = 7√2, but √2 + √3 cannot be combined.

Worked example

Common mistakes

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