Rationalization

Rationalizing The Denominator

$\frac{1}{\sqrt{2}}$ = $\frac{1}{\sqrt{2}}\ast \frac{\sqrt{2}}{\sqrt{2}}$ = $\frac{\sqrt{2}}{2}$

Why it is important

If you don’t, it messes up the limits. Example: $\frac{x-4}{\sqrt{x}-2}$ when x = 4, it will be $\frac{0}{0}$ This doesn’t really tell us anything. There is a hole at x=4 $\frac{(x-4)(\sqrt{x}+2)}{x-4}$ = $\frac{\sqrt{x}+2}{1}$

Law of rationalization

$\frac{a}{\sqrt{a}}$ = $\sqrt{a}$