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Maths

Surds - Higher

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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

Simplify square root of 12 + square root of 75

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Answer

square root of 12 + square root of 75 = square root of 4 x square root of 3 + square root of 3 x square root of 25 = 2 square root of 3 + 5 square root of 3

(You can treat the square root of 3 like a letter in algebra.)

= 7 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

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