well, the idea is to "rationalize the denominator", which is another way to say "getting rid of that pesky radical in the bottom".
so, we'll do so by multiplying for "something" that raises the radicand and then it comes out
[tex]\bf \cfrac{8}{8\sqrt{3}}\implies \cfrac{1}{\sqrt{3}}\implies \stackrel{rationalizing~it}{\cfrac{1}{\sqrt{3}}\cdot \cfrac{\sqrt{3}}{\sqrt{3}}}\implies \cfrac{1\sqrt{3}}{(\sqrt{3})^2}\implies \cfrac{\sqrt{3}}{3}[/tex]
bear in mind that [tex]\bf \cfrac{something}{something}=1\qquad \qquad \cfrac{same}{same}=1\qquad \qquad \cfrac{\sqrt{3}}{\sqrt{3}}=1[/tex]
so, all we really did was, multiply it by "1", and recall that anything times 1 is just itself, so the fraction never really changed in value, just looks different, is all.
