To find the product of \( \sqrt{12} \) and \( 56 \), we can start by calculating \( \sqrt{12} \).
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First, simplify \( \sqrt{12} \): \[ \sqrt{12} = \sqrt{4 \cdot 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3} \]
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Now find the product with \( 56 \): \[ \sqrt{12} \times 56 = 2\sqrt{3} \times 56 = 112\sqrt{3} \]
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Now, let's calculate \( 112\sqrt{3} \) numerically. Knowing that \( \sqrt{3} \approx 1.732 \): \[ 112\sqrt{3} \approx 112 \times 1.732 \approx 193.824 \]
Since \( \sqrt{3} \) is an irrational number, the product \( 112\sqrt{3} \) is also an irrational number.
Now, since the question likely requires one of the given options, let's provide an approximate decimal value for \( 112\sqrt{3} \). Calculating it more precisely: \[ 112 \times 1.73205080757 \approx 193.828 \]
None of the options you provided directly matches this value, but the important conclusion here is that the product of \( \sqrt{12} \) and \( 56 \) results in an irrational number.
Thus, the answer would be:
- The product \( 112\sqrt{3} \), an irrational number.
If you need to choose one of the provided options, please check again, as it looks like the products provided don't match the calculated value.