To find the product of \( \sqrt{12} \) and \( 56 \), we first calculate \( \sqrt{12} \).
We know that:
\[ \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3} \]
Next, we compute the product:
\[ \sqrt{12} \times 56 = (2\sqrt{3}) \times 56 = 112\sqrt{3} \]
Now we need to find the approximate value of \( 112\sqrt{3} \). The value of \( \sqrt{3} \) is approximately \( 1.732 \).
Now we calculate:
\[ 112 \times 1.732 \approx 193.984 \]
So, \( 112\sqrt{3} \approx 193.984 \), which is a whole number multiplied by an irrational number \( \sqrt{3} \).
Thus, \( 112\sqrt{3} \) is an irrational number.
The product \( 112\sqrt{3} \) is not one of the provided numerical options, but it is classified as an irrational number. Therefore, you can summarize the answer as follows:
- Approximately \( 193.984 \); an irrational number.
None of the provided options are correct as they do not match the calculated product.
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