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Maths

Surds - Higher

Basic rules

A surd is a square root which cannot be reduced to a whole number. For example, square root of 4 = 2 is not a surd, as the answer is a whole number. But square root of 5 is not a whole number. You could use a calculator to find that square root of 5 = 2.236067977 but instead of this we often leave our answers in the square root form, as a surd.

You need to be able to simplify expressions involving surds. Here are some general rules that you will need to learn.

square root of ab = square root of a x square root of b

square root of a x square root of a = a

Activity

Feeling confident? Test yourself in a quick game of before trying some questions for yourself below.

Now have a look at some questions.

Question

Simplify square root of 12

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Answer

square root of 12= square root of 4 x square root of 32 square root of 3

Question

Simplifysquare root of 12 x square root of 3

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Answer

square root of 12 x square root of 3 = square root of (12 x 3) = square root of 36 = 6

Question

Simplifysquare root of 12 over square root of 6

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Answer

square root of 12 over square root of 6

= square root of 12 over 6

(in general square root of a over  square root of b =  square root of a over b)

square root of 2

Rationalising

Rationalising an expression means getting rid of any surds from the bottom of fractions. Usually when you are asked to simplify an expression it means you should also rationalise it.

Question

Simplify square root of 8 over square root of 6

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Answer

square root of 8 over square root of 6

square root of 8 x square root of 8 over square root of 6 x square root of 6

(square root of 48) over 6

= square root of 16 x 3 over 6

4 square root of 3 over 6

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