Fiducia TogetherSurds
A root that cannot be simplified to a whole number, left in root form to stay exact.
Please note: This page explains a word or a process in education. It is general information about the system, the law and the guidance in England — not advice about your child, your school or your exam. If a decision is going against you, get advice from one of the free services we link to before you agree to anything or miss a deadline. If you are revising, check your own exam board's specification: boards word things differently and yours is the one that marks you.
What it is
A surd is an irrational root written as a root: √2, 3√5, √50. Leaving it as a surd keeps the value exact, where a decimal would round it.
Where it applies
Higher tier maths, and it appears in trigonometry and Pythagoras answers.
How it works
Simplifying means pulling out square factors: √50 = √25 × √2 = 5√2.
Rationalising the denominator means removing a surd from the bottom of a fraction by multiplying top and bottom by it — or by the conjugate where the denominator is a sum.
How to use it in your work
When a question says "give your answer in exact form" or "in surd form", a decimal scores nothing however accurate.
Always simplify fully. 5√2 and √50 are equal and only one of them gets the mark.
Where to get help
Your teacher, your board's specification for what is on your paper, and Bitesize for worked examples. The maths song runs the topics in order.
Revise this with a song
These are ours. We write revision songs because a lot of people remember a tune when they cannot remember a page, and because revising out loud in the kitchen beats staring at a highlighter.
- The Maths Song The GCSE maths topics, in order.
Where to read more
Last reviewed 2026-08-28 by Fiducia Together · Next review due 2027-08-28
Please note: This page explains a word or a process in education. It is general information about the system, the law and the guidance in England — not advice about your child, your school or your exam. If a decision is going against you, get advice from one of the free services we link to before you agree to anything or miss a deadline. If you are revising, check your own exam board's specification: boards word things differently and yours is the one that marks you.