Question

simplify the following radical expressions.

square root of 72

Answer 1

To simplify the square root of 72, we start by factoring 72 into its prime factors:

\[
72 = 36 \times 2 = 6^2 \times 2
\]

Now, we can write the square root of 72 as:

\[
\sqrt{72} = \sqrt{36 \times 2}
\]

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

\[
\sqrt{72} = \sqrt{36} \times \sqrt{2}
\]

Since \(\sqrt{36} = 6\), we can simplify further:

\[
\sqrt{72} = 6 \sqrt{2}
\]

Thus, the simplified form of \(\sqrt{72}\) is:

\[
\boxed{6\sqrt{2}}
\]