Originally Posted by

**ejanderson** 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: $\displaystyle \sqrt\frac{m^4n^8}{81p^2}$ which I beleive = $\displaystyle \frac{m^2n^4}{9p}$

I'm having some trouble in understanding the procedure when the numerator and or denominator are not perfect squares...such as $\displaystyle \sqrt\frac{3}{8}$. 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 $\displaystyle \sqrt\frac{24}{8}$. This I understand, what I don't understand is the following (I don't know if it would be called simplification or not?) $\displaystyle \sqrt\frac{24}{8}$ = $\displaystyle \frac{2\sqrt6}{8}$ I do not understand $\displaystyle 2\sqrt6$ in the numerator. How do they come to this conclusion and why can't you leave it as $\displaystyle \sqrt\frac{24}{8}$?

Any help would be greatly appreciated as always!