Question

Divide: 9 Square root 33 divided by27 square root of 11
• Provide an exact answer. (1 point)

Answer 1

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

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

Next, we can simplify this fraction. First, we can divide the coefficients (the numbers in front of the square roots):

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

Now, we can rewrite the expression as:

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

Next, we can simplify the square root fraction:

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

Combining these results gives us:

\[
\frac{1}{3} \sqrt{3}
\]

Therefore, the exact answer is:

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