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