Question

Simplify the following radical expressions. √60 (1 point)

Answer 1

To simplify the radical expression \(\sqrt{60}\), we can start by factoring 60 into its prime factors.

The prime factorization of 60 is:
\[
60 = 2^2 \times 3 \times 5
\]

Next, we can express \(\sqrt{60}\) in terms of these prime factors:
\[
\sqrt{60} = \sqrt{2^2 \times 3 \times 5}
\]

Using the property of square roots that \(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\), we can separate the square root:
\[
\sqrt{60} = \sqrt{2^2} \times \sqrt{3} \times \sqrt{5}
\]

Since \(\sqrt{2^2} = 2\), we get:
\[
\sqrt{60} = 2 \times \sqrt{3} \times \sqrt{5}
\]

Now we can combine \(\sqrt{3} \times \sqrt{5}\):
\[
\sqrt{3} \times \sqrt{5} = \sqrt{15}
\]

Therefore:
\[
\sqrt{60} = 2\sqrt{15}
\]

Thus, the simplified form of \(\sqrt{60}\) is:
\[
\boxed{2\sqrt{15}}
\]