Question

Four radical six times two radical 18 simplest form

Answer 1

To simplify the expression \(4\sqrt{6} \times 2\sqrt{18}\), we can follow these steps:

1. **Multiply the coefficients and the radicals separately:**

\[
4 \times 2 = 8
\]
\[
\sqrt{6} \times \sqrt{18} = \sqrt{6 \times 18} = \sqrt{108}
\]

2. **Combine the results:**

\[
8\sqrt{108}
\]

3. **Simplify \(\sqrt{108}\):**

First, we factor \(108\):
\[
108 = 36 \times 3 = 6^2 \times 3
\]
Therefore:
\[
\sqrt{108} = \sqrt{36 \times 3} = \sqrt{36} \times \sqrt{3} = 6\sqrt{3}
\]

4. **Substitute back into the expression:**

Now we have:
\[
8\sqrt{108} = 8 \times 6\sqrt{3} = 48\sqrt{3}
\]

Thus, the simplest form of \(4\sqrt{6} \times 2\sqrt{18}\) is \(\boxed{48\sqrt{3}}\).