Question

simplify the following radical expression

square root of 60

Answer 1

To simplify the square root of 60, we can factor 60 into its prime factors:

\[ 60 = 2^2 \times 3 \times 5 \]

Now, we can express the square root as follows:

\[
\sqrt{60} = \sqrt{2^2 \times 3 \times 5}
\]

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

\[
\sqrt{60} = \sqrt{2^2} \times \sqrt{3 \times 5}
\]

Calculating the square root of \(2^2\):

\[
\sqrt{60} = 2 \times \sqrt{15}
\]

Thus, the simplified form of \(\sqrt{60}\) is:

\[
\boxed{2\sqrt{15}}
\]