Question

Which is equivalent to left-parenthesis 5 StartRoot 2 EndRoot right-parenthesis left-parenthesis 3 StartRoot 6 EndRoot right-parenthesis?

Answer options with 5 options
A.
8 StartRoot 8 EndRoot

B.
8 StartRoot 12 EndRoot

C.
15 StartRoot 8 EndRoot

D.
30 StartRoot 3 EndRoot

E.
60 StartRoot 3 EndRoot

Answer 1

To simplify the expression \((5 \sqrt{2})(3 \sqrt{6})\), we can first multiply the numerical coefficients (5 and 3) and then the square roots (\(\sqrt{2}\) and \(\sqrt{6}\)).

1. Multiply the coefficients:
\[
5 \times 3 = 15
\]

2. Multiply the square roots:
\[
\sqrt{2} \times \sqrt{6} = \sqrt{2 \times 6} = \sqrt{12}
\]

3. Combine the two results:
\[
(5 \sqrt{2})(3 \sqrt{6}) = 15 \sqrt{12}
\]

Now, we can simplify \(\sqrt{12}\):
\[
\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}
\]

Now, substitute this back into our expression:
\[
15 \sqrt{12} = 15 \times 2 \sqrt{3} = 30 \sqrt{3}
\]

Therefore, the equivalent expression is:
\[
30 \sqrt{3}
\]

Looking at the answer options, the correct choice is:
**D. \(30 \sqrt{3}\)**