Question

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

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 use the properties of multiplication.

1. First, multiply the constants (5 and 3):
\[
5 \times 3 = 15
\]

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

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

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

So, substituting this back, we have:
\[
15\sqrt{12} = 15 \times 2\sqrt{3} = 30\sqrt{3}
\]

Therefore, the equivalent expression of \( (5\sqrt{2})(3\sqrt{6}) \) is:
\[
30\sqrt{3}
\]

Thus, the correct answer is:
**D. \( 30\sqrt{3} \)**.