simplify the following radical expression

square root of 60

1 answer

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:

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

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