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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 CCEA GCSE Maths Surds: explanations and worked examples.
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Simplify 80\sqrt{80}80 fully.