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Step-by-step explanation:
To compare \(2\sqrt{60}\) and \(3\sqrt{4}\), let's simplify each expression.
1. \(2\sqrt{60}\):
\[ 2\sqrt{60} = 2 \times \sqrt{60} = 2 \times \sqrt{4 \times 15} = 2 \times \sqrt{4} \times \sqrt{15} = 2 \times 2 \times \sqrt{15} = 4\sqrt{15} \]
2. \(3\sqrt{4}\):
\[ 3\sqrt{4} = 3 \times \sqrt{4} = 3 \times 2 = 6 \]
Now, we compare \(4\sqrt{15}\) and \(6\).
Next, approximate \(\sqrt{15}\):
\[ \sqrt{15} \approx 3.87 \]
Then:
\[ 4\sqrt{15} \approx 4 \times 3.87 = 15.48 \]
So, \(4\sqrt{15} \approx 15.48\) is greater than 6.
Therefore, \(2\sqrt{60}\) is greater than \(3\sqrt{4}\).