To simplify the square root of 60, we can start by factoring 60 into its prime factors.
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The prime factorization of 60 is: \[ 60 = 2^2 \times 3 \times 5 \]
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We can now express the square root: \[ \sqrt{60} = \sqrt{2^2 \times 3 \times 5} \]
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Using the property of square roots that states \(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\), we can separate the factors: \[ \sqrt{60} = \sqrt{2^2} \times \sqrt{3} \times \sqrt{5} \]
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Simplifying \(\sqrt{2^2}\): \[ \sqrt{60} = 2 \times \sqrt{3} \times \sqrt{5} \]
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Now, combining \(\sqrt{3} \times \sqrt{5}\): \[ \sqrt{60} = 2 \times \sqrt{15} \]
Thus, the simplified form of \(\sqrt{60}\) is: \[ \sqrt{60} = 2\sqrt{15} \]
This is the exact answer.
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