Question

Simplify: 3 the square root of 108

Answer 1

To simplify \( 3 \sqrt{108} \), we can start by simplifying \( \sqrt{108} \).

First, we can factor \( 108 \):
\[
108 = 36 \times 3 = 6^2 \times 3
\]

Now, we can take the square root:
\[
\sqrt{108} = \sqrt{36 \times 3} = \sqrt{36} \times \sqrt{3} = 6\sqrt{3}
\]

Now we substitute this back into the expression:
\[
3 \sqrt{108} = 3 \times 6\sqrt{3} = 18\sqrt{3}
\]

Thus, the simplified form of \( 3 \sqrt{108} \) is:
\[
\boxed{18\sqrt{3}}
\]