I'm having some difficulty in understanding the following square root "procedure".

When finding the square root of a fraction, it's pretty easy when both the numerator and denominator are perfect squares:

which I beleive =

I'm having some trouble in understanding the procedure when the numerator and or denominator are not perfect squares...such as

. The way I understand it is, I need to multiply the numerator by the number that would make the number in the denominator a perfect square. Since 8 is the square root of 64, I need to multiply the numerator, 3, by 8, which gives 24. So I then have the following

. This I understand, what I don't understand is the following (I don't know if it would be called simplification or not?)

=

I do not understand

in the numerator. How do they come to this conclusion and why can't you leave it as

?

Any help would be greatly appreciated as always!