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Surds

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A surd is an irrational root left in exact form, such as 2\sqrt{2}2​ or 5\sqrt{5}5​. A square root like 36\sqrt{36}36​ is not a surd because it simplifies exactly to 666.

When simplifying, look for the largest square number factor inside the root. You may split multiplication, so ab=ab\sqrt{ab} = \sqrt{a}\sqrt{b}ab​=a​b​ for positive numbers, but you must not split addition, so 9+16≠9+16\sqrt{9+16} \ne \sqrt{9}+\sqrt{16}9+16​=9​+16​.

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Question 1

2 marks

Write 48 \sqrt{48}\,48​ in the form k3k\sqrt{3}k3​, where k k\,k is an integer.

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What is a surd?

Surds Revision Guide

  1. GCSE
  2. /Maths
  3. /Surds

Revision notes for CCEA GCSE Maths Surds: explanations and worked examples.

Practise questions

1 of 5

Simplify 80\sqrt{80}80​ fully.