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Express the square root of 640 in the form π root π, where π and π are integers and π takes the least possible value.
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In order to simplify the surd root 640, we need to consider the square numbers and which of these are factors of 640.
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In particular, weβre looking for the highest factor of 640 that is also a square number or perfect square.
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In this case, the highest factor of 640 is 64.
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As 64 multiplied by 10 is 640, we can rewrite the square root of 640 as the square root of 64 multiplied by the square root of 10.
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The square root of 64 is equal to eight as eight multiplied by eight is 64.
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Therefore, we can simplify square root 64 multiplied by square root 10 as eight multiplied by root 10 or eight root 10.
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To check whether π has taken its least possible value, we need to look at our square numbers again.
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Apart from one, do any of the square numbers divide exactly into 10?
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Well, we know that four and nine are not factors of 10.
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And seen as all the other numbers are larger than 10, 10 is the lowest value or least possible value of π.
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This means that the simplest form of the square root of 640 is eight square root 10 or eight root 10.