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Surds are square roots that cannot be reduced to a whole number e.g.

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there are a few simple rules that we have to learn for surds

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x=

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This means that if we have a question such as solve x

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we put the 2 and the 8 inside the square root to get =

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now we know that = 4

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so 4 is our final answer

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Rule 2 is very similar.....

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it just states that =

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e.g. = = =2

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another type of question that you sometimes get asked is where you have to 'rationalise the denominator'

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this means that if there is a surd in the denominator part of a fraction, you have to make it a 'rational' (whole) number

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e.g.

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to rationalise the denominator we have to multiply both the top and the bottom of the fraction by

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so we get

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now, due to another rule which states that our

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and we leave the surd on the top

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so now we have

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