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GCSE

Positive and Negative Integers

Question

How do you estimate a square root?

2 years ago

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Hazel Howe


1 Answer

Devan-Kumar M Profile Picture
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You can estimate a square root by seeing what square numbers you can recognise in the region above or below it. E.G. You may wish to estimate the square root of 26 and wonder it must be more than 5 as 26>25=5^2 and less than 6 as 26<36=6^2. Note therefore 5^2< 26 < 6^2. Then you may note how much closer 26 is to 25 than 36. In fact it is roughly a 10th of the way between 25 and 36. Thus you may estimate the square root is a 10th of the way between 5 and 6, e.g. 5.1.

Note 5.1^2 = 26.01 so this is an extremely accurate approximation.

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