To simplify \(\frac{\sqrt{60}}{2\sqrt{5}}\), we can follow these steps:
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First, simplify \(\sqrt{60}\): \[ \sqrt{60} = \sqrt{4 \times 15} = \sqrt{4} \times \sqrt{15} = 2\sqrt{15} \]
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Now we substitute \(\sqrt{60}\) in the original expression: \[ \frac{\sqrt{60}}{2\sqrt{5}} = \frac{2\sqrt{15}}{2\sqrt{5}} \]
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The 2 in the numerator and denominator cancel out: \[ = \frac{\sqrt{15}}{\sqrt{5}} \]
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We simplify \(\frac{\sqrt{15}}{\sqrt{5}}\): \[ = \sqrt{\frac{15}{5}} = \sqrt{3} \]
Now let's look at the options provided:
A. \(\frac{\sqrt{30}}{\sqrt{5}}\) simplifies to \(\sqrt{6}\) which is not equivalent to \(\sqrt{3}\).
B. \(\frac{12}{2\sqrt{5}}\) simplifies to \(\frac{6}{\sqrt{5}}\) which is not equivalent to \(\sqrt{3}\).
C. \(\frac{\sqrt{12}}{2}\) simplifies to \(\frac{2\sqrt{3}}{2} = \sqrt{3}\), which is equivalent.
D. \( \frac{12}{2} = 6\), which is not equivalent to \(\sqrt{3}\).
The correct option is: C. \(\frac{\sqrt{12}}{2}\)