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So if you put a square root sign around a number that is not a square number, then what you have written is a surd.

e.g. √10 is a surd, because 10 is not a square number. √9 is not a surd, because 9 is a square number, so you can write √9= 3

Even if the number under the square root sign is not a square number, it can still be simplified.

Write the starting number as a product of two new numbers, where one of them is a square number (e.g. 45 -> 9 x 5).  Take the root of the square number, and write it outside of the root sign

e.g. √45 = √(9×5)=3√5

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AQA Unit 2 March 2011 (H) - Page 11, Question 17

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