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

Question

Square root of 6 Times Square root of 8

Answer 1

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

So, we have:

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

Calculating \(6 \times 8\):

\[ 6 \times 8 = 48 \]

Now, we have:

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

Next, we need to simplify \(\sqrt{48}\). We can factor \(48\) into \(16\) and \(3\):

\[ 48 = 16 \times 3 \]

Now, we can simplify \(\sqrt{48}\):

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

So the final answer is:

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