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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=ab 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.
Question 1
2 marksWrite 48 \sqrt{48}\,48 in the form k3k\sqrt{3}k3, where k k\,k is an integer.
What is a surd?
Revision notes for Edexcel GCSE Maths Surds. Open the guide for explanations and worked examples. Written against the Edexcel GCSE Maths (1MA1) specification, so the content matches what's examinable rather than general Maths background.
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Simplify 80\sqrt{80}80 fully.