# How do you simplify 33/sqrt99?

Mar 19, 2017

#### Answer:

$\sqrt{11}$

#### Explanation:

$\sqrt{99} = \sqrt{9 \times 11} = \sqrt{9} \times \sqrt{11} = 3 \sqrt{11}$

$\Rightarrow \frac{33}{\sqrt{99}} = {\cancel{33}}^{11} / \left({\cancel{3}}^{1} \sqrt{11}\right) = \frac{11}{\sqrt{11}}$

$\textcolor{b l u e}{\text{ Rationalising the denominator}}$

$\Rightarrow \frac{11}{\sqrt{11}} \times \frac{\sqrt{11}}{\sqrt{11}}$

$= \frac{{\cancel{11}}^{1} \sqrt{11}}{\cancel{11}} ^ 1$

$= \sqrt{11}$

Mar 19, 2017

We can also do this in one fell swoop using prime factorization:

$\frac{33}{\sqrt{99}} = \frac{3 \times 11}{{3}^{2} \times 11} ^ \left(\frac{1}{2}\right) = \frac{3 \times 11}{3 \times {11}^{\frac{1}{2}}} = {11}^{1 - \frac{1}{2}} = {11}^{\frac{1}{2}} = \sqrt{11}$