To find the product of \( \sqrt{12} \) and \( 56 \), we first calculate \( \sqrt{12} \):
\[ \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3} \]
Now, we multiply \( 2\sqrt{3} \) by \( 56 \):
\[ 2\sqrt{3} \times 56 = 112\sqrt{3} \]
Next, we can approximate \( \sqrt{3} \) to calculate \( 112\sqrt{3} \):
\[ \sqrt{3} \approx 1.732 \]
Therefore,
\[ 112\sqrt{3} \approx 112 \times 1.732 \approx 193.184 \]
So, the approximate value of the product is \( 193.184 \), which is not listed in your options and does not match any of the provided decimal numbers. However, the product \( 112\sqrt{3} \) is indeed an irrational number since it involves the square root of 3.
If we strictly need to select from the provided options, it seems there is a misunderstanding or misrepresentation of the question, as none of those options accurately reflect the product of \( 56\sqrt{12} \).