Question

Find the square root of 45. Make sure your answer is in the simplest radical form.

Answer 1

To find the square root of 45 in simplest radical form, we start by factoring 45 into its prime factors:

\[
45 = 9 \times 5 = 3^2 \times 5
\]

Now, we can take the square root:

\[
\sqrt{45} = \sqrt{9 \times 5}
\]

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

\[
\sqrt{45} = \sqrt{9} \times \sqrt{5}
\]

Since \(\sqrt{9} = 3\), we can substitute that in:

\[
\sqrt{45} = 3 \times \sqrt{5}
\]

Thus, the square root of 45 in simplest radical form is:

\[
\boxed{3\sqrt{5}}
\]