To find the product of \(\sqrt{12}\) and \(56\), we first compute \(\sqrt{12}\).
\[ \sqrt{12} = \sqrt{4 \cdot 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3} \]
Now, we can calculate the product:
\[ \sqrt{12} \times 56 = 56 \times 2\sqrt{3} = 112\sqrt{3} \]
Now, to determine what type of number \(112\sqrt{3}\) is, we know that \(\sqrt{3}\) is an irrational number. The product of a rational number (112) and an irrational number (\(\sqrt{3}\)) is also an irrational number.
Thus, \(112\sqrt{3}\) is an irrational number.
To find a numerical approximation, we can use \(\sqrt{3} \approx 1.732\):
\[ 112\sqrt{3} \approx 112 \times 1.732 \approx 193.184 \]
However, none of the provided options seem to match this product or its approximation.
Among the provided responses, none of them correctly represent \(112\sqrt{3}\). The correct answer is that it is an irrational number, but the specific numerical approximations are not accurate according to the simple calculation above.
If you're looking for what type of number it is, the answer is:
\(112\sqrt{3}\); an irrational number.
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