Question

preform the indicated operation. be sure to rationalize the denominator when necessary.make sure to simplify as much as possible and givw the exact answer (this means NO decimals since decimals is rounding!)
3 square root of 5 times 7 square root of 11

Answer 1

To perform the operation \( 3 \sqrt{5} \times 7 \sqrt{11} \), we can follow these steps:

1. **Multiply the coefficients (the numbers outside the square roots)**.
2. **Multiply the square roots together**.

So we have:

\[
3 \sqrt{5} \times 7 \sqrt{11} = (3 \times 7) \times (\sqrt{5} \times \sqrt{11})
\]

Calculating the coefficients:

\[
3 \times 7 = 21
\]

Now for the square roots:

\[
\sqrt{5} \times \sqrt{11} = \sqrt{5 \times 11} = \sqrt{55}
\]

Putting it all together:

\[
3 \sqrt{5} \times 7 \sqrt{11} = 21 \sqrt{55}
\]

Thus, the exact answer (in its simplest form) is:

\[
\boxed{21 \sqrt{55}}
\]