To find the product of \( \sqrt{12} \) and \( 56 \):
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Calculate \( \sqrt{12} \): \[ \sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3} \]
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Then calculate the product: \[ 56 \times \sqrt{12} = 56 \times 2\sqrt{3} = 112\sqrt{3} \]
Now, we need the approximate decimal value of \( 112\sqrt{3} \).
Using \( \sqrt{3} \approx 1.732 \): \[ 112 \times 1.732 \approx 193.184 \]
Thus, we have \( 112\sqrt{3} \approx 193.184 \).
Since \( \sqrt{3} \) is an irrational number, \( 112\sqrt{3} \) is also an irrational number.
However, none of the provided responses match this calculation. It seems you may need to recheck the options given. If taking into account possible approximations, confirm the calculations to ascertain if any of the provided numerical options are accurate. If strictly checking those options without recalculating, then none provided are correct since they don't reflect the described product.
Thus, you can conclude that \( 112\sqrt{3} \) is approximately \( 193.184 \) and is an irrational number, but none of the given choices accurately matched this product.