Simplify.

Remove all perfect squares from inside the square root.
\[\sqrt{18}=\]

1 answer

To simplify \(\sqrt{18}\), we start by factoring \(18\) into its prime factors.

\[ 18 = 9 \times 2 \]

Next, we note that \(9\) is a perfect square (\(3^2\)). We can rewrite the square root as follows:

\[ \sqrt{18} = \sqrt{9 \times 2} \]

Applying the property of square roots \(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\), we have:

\[ \sqrt{18} = \sqrt{9} \times \sqrt{2} \]

Since \(\sqrt{9} = 3\), we can simplify further:

\[ \sqrt{18} = 3 \times \sqrt{2} \]

Thus, the final simplified form of \(\sqrt{18}\) is:

\[ \boxed{3\sqrt{2}} \]