To find the product of \( \sqrt{12} \) and \( 56 \), we can first calculate \( \sqrt{12} \).
\[ \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3} \]
Now, we can multiply this by \( 56 \):
\[ 56 \times \sqrt{12} = 56 \times 2\sqrt{3} = 112\sqrt{3} \]
Next, let's calculate \( 112\sqrt{3} \). We know that \( \sqrt{3} \) is approximately \( 1.732 \):
\[ 112 \times 1.732 \approx 193.184 \]
Thus, the number is about \( 193.184 \), which is not one of the options you've provided. However, we can determine the type of number.
Since \( \sqrt{3} \) is an irrational number and the product of a rational number (112) and an irrational number (\(\sqrt{3}\)) is also an irrational number, we conclude:
The product \( 112\sqrt{3} \) is an irrational number.
None of the numerical options given in the question perfectly match the product, but they all indicate an irrational number. Depending on the context of your question, it looks like there might be an inconsistency in the given options.
If the focus is on what type of number the product is, the answer is: an irrational number.
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