Question

preform the indicated operation. be sure to rationalize the denominator when necessary. Also, remember to simplify as needed. Give your answer as an exact answer.
square root of 6 times square root of 8

Answer 1

To perform the operation \(\sqrt{6} \times \sqrt{8}\), we can use the property of square roots that states \(\sqrt{a} \times \sqrt{b} = \sqrt{a \cdot b}\).

So, we have:

\[
\sqrt{6} \times \sqrt{8} = \sqrt{6 \cdot 8} = \sqrt{48}
\]

Next, we simplify \(\sqrt{48}\). We can factor \(48\) to find perfect squares:

\[
48 = 16 \times 3
\]

Thus:

\[
\sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3}
\]

Therefore, the final answer is:

\[
\sqrt{6} \times \sqrt{8} = 4\sqrt{3}
\]

This result is already in its simplest form, and there was no need to rationalize the denominator since there was none involved.