Answer:
B
Explanation:
The volume of a rectangular prism is the length times width times height.
V = LWH
V = (4√3)(3√6)W
V = 12√18 W
V = 36√2 W
If the volume is irrational, then W cannot have a radical that is half of a perfect square, because when multiplied by √2, that would yield a rational volume. For example, √18 × √2 = √36 = 6.
Therefore, the answer must be B, because 12 is not half of a perfect square.
V = 36√2 (4√12)
V = 144√24
V = 288√6