Question

Divide 9√33 by 27√11. Give an exact Answer.

Answer 1

To divide \( 9\sqrt{33} \) by \( 27\sqrt{11} \), we can write the expression as follows:

\[
\frac{9\sqrt{33}}{27\sqrt{11}}
\]

We can simplify this fraction step by step.

1. **Simplify the coefficients**: The coefficients \( 9 \) and \( 27 \) can be simplified:

\[
\frac{9}{27} = \frac{1}{3}
\]

2. **Combine the square roots**: Now we can rewrite the fraction with the square roots:

\[
\frac{\sqrt{33}}{\sqrt{11}}
\]

3. **Simplify the square roots**: We can simplify this further:

\[
\frac{\sqrt{33}}{\sqrt{11}} = \sqrt{\frac{33}{11}} = \sqrt{3}
\]

Putting it all together, we have:

\[
\frac{9\sqrt{33}}{27\sqrt{11}} = \frac{1}{3} \cdot \sqrt{3}
\]

Thus, the final simplified result is:

\[
\frac{\sqrt{3}}{3}
\]

So the exact answer is:

\[
\frac{\sqrt{3}}{3}
\]