Question

What is the product of the following in simplest radical form for radical six times two radical 18

Answer 1

To simplify the product of \( \sqrt{6} \times 2\sqrt{18} \), we can first rewrite the expression:

\[
\sqrt{6} \times 2\sqrt{18} = 2\sqrt{6} \times \sqrt{18}
\]

Next, we can combine the square roots:

\[
2\sqrt{6 \times 18}
\]

Now, we need to calculate \( 6 \times 18 \):

\[
6 \times 18 = 108
\]

Thus, we have:

\[
2\sqrt{108}
\]

Next, we simplify \( \sqrt{108} \). First, we factor \( 108 \):

\[
108 = 36 \times 3
\]
So, we can write:

\[
\sqrt{108} = \sqrt{36 \times 3} = \sqrt{36} \times \sqrt{3} = 6\sqrt{3}
\]

Now, substituting this back into our expression gives us:

\[
2\sqrt{108} = 2 \times 6\sqrt{3} = 12\sqrt{3}
\]

Thus, the product of \( \sqrt{6} \times 2\sqrt{18} \) in simplest radical form is:

\[
\boxed{12\sqrt{3}}
\]