Question

Perform the indicated operation. Be sure to rationalize the denominator when necessary. Also, remember to simplify as needed. Give your answer as an exact answer. √6.√8 (1 point)

Answer 1

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

So, we have:

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

Calculating the product inside the square root:

\[
6 \cdot 8 = 48
\]

Thus, we have:

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

Next, we simplify \(\sqrt{48}\). We can factor 48 into its prime factors:

\[
48 = 16 \cdot 3 = 4^2 \cdot 3
\]

Now we can take the square root:

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

Therefore, the exact simplified answer is:

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