To find the product of \( \sqrt{12} \) and \( 56 \), we first calculate \( \sqrt{12} \).
We know that: \[ \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3} \]
Now, we compute the product: \[ \sqrt{12} \times 56 = 2\sqrt{3} \times 56 = 112\sqrt{3} \]
Next, we need to find an approximate value for \( \sqrt{3} \). The approximate value of \( \sqrt{3} \) is about \( 1.732 \). Therefore, \[ 112\sqrt{3} \approx 112 \times 1.732 \approx 193.184 \]
Since \( 112\sqrt{3} \) involves the square root of a non-perfect square (3), \( 112\sqrt{3} \) is also an irrational number.
Among the available response options, none of the numerical approximations provided perfectly match \( 112\sqrt{3} \). However, the conclusion is that the product \( \sqrt{12} \times 56 \) is an irrational number.
The answer will therefore acknowledge that the product is an irrational number with an approximate evaluation of around \( 193.184 \) (but exact choices aren't provided). The correct classification is as follows:
112sqrt(3) ; an irrational number.