How do you simplify #sqrt(18)# without a calculator?

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Answer 1 · 2015-02-02T10:16:25

One way to simplify this number is to look for alternative ways of writing the number that's under the square root sign.

You must extract the square root from #"18"#, which isn't a perfect square. However, if you look closely at this number you'll find that

#18 = 9 * 2#

You know that #"9"# is a perfect square, which means that

#18 = 3^(2) * 2#

Stick this under the square root and you'll get

#sqrt(18) = sqrt(3^(2) * 2) = sqrt(3^(2)) * sqrt(2) = 3sqrt(2)#