You would multiply top and bottom by [tex]\sqrt{3}[/tex] to go from [tex]\frac{1}{\sqrt{3}}[/tex] to [tex]\frac{\sqrt{3}}{3}[/tex]
Multiplying a square root by itself is the same as squaring the value.
So, [tex]\sqrt{x}*\sqrt{x} = (\sqrt{x})^2 = x, \ \ \text{ when } x \ge 0[/tex]
Which is why we're able to get rid of the square root in the denominator. The square root and squaring operation effectively cancel each other out.
