To simplify \(\frac{\sqrt{60}}{2\sqrt{5}}\), we start by simplifying the expression step by step:
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Simplify \(\sqrt{60}\): \[\sqrt{60} = \sqrt{12 \cdot 5} = \sqrt{12}\sqrt{5} = 2\sqrt{3}\sqrt{5} = 2\sqrt{15}\]
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Substitute into the expression: \[\frac{\sqrt{60}}{2\sqrt{5}} = \frac{2\sqrt{15}}{2\sqrt{5}}\]
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Cancel the 2 in the numerator and denominator: \[\frac{2\sqrt{15}}{2\sqrt{5}} = \frac{\sqrt{15}}{\sqrt{5}}\]
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Simplify further: \[\frac{\sqrt{15}}{\sqrt{5}} = \sqrt{\frac{15}{5}} = \sqrt{3}\]
Therefore, the simplified form of \(\frac{\sqrt{60}}{2\sqrt{5}} = \sqrt{3}\).
Now, none of the options directly match \(\sqrt{3}\). However, let's re-examine the options:
A. \(\frac{\sqrt{30}}{2\sqrt{5}}\) does not equal \(\sqrt{3}\). B. \(\frac{12}{2\sqrt{5}} = \frac{6}{\sqrt{5}}\) and does not equal \(\sqrt{3}\). C. \(\frac{\sqrt{12}}{2} = \frac{2\sqrt{3}}{2} = \sqrt{3}\) which matches. D. \(\frac{12}{2} = 6\) and does not equal \(\sqrt{3}\).
Thus, the correct answer is C. \(\frac{\sqrt{12}}{2}\).