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May 28, 2015

Homework Help: Math

Posted by Emily on Monday, February 12, 2007 at 8:56am.

How do you find a square root of a number that's not a perfect square? I'm very confused. The book doesn't explain it too well.

You can approximate it or simplify it in terms of (products of) square roots of smaller numbers.

E.g. consider sqrt[117]

The number 177 can be factored:

117 = 9*13

So we have:

sqrt[177] = sqrt[9*13] =
sqrt[9]*sqrt[13] = 3 sqrt[13]

Cases like:

sqrt[a]/sqrt[b]

can be rewritten by multiplying numerator and denominator by sqrt[b]:

sqrt[a]/sqrt[b] =

sqrt[a]*sqrt[b]/(sqrt[b]*sqrt[b]) =

sqrt[a]*sqrt[b]/b

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