Which expression is equivalent to √32x^6?
A. 4x^3√2
B. 8x^3
C.
4x√2
D. 16x^3
The expression √32x^6 can be simplified as follows:
√32x^6 = √(16 * 2 * x^6) (breaking down 32 into its prime factors)
= √(4^2 * 2 * x^6) (since 16 = 4^2)
= 4 * √(2 * x^6) (taking the square root of the perfect square)
= 4 * √(2) * √(x^6) (splitting the square root)
= 4 * √(2) * x^3 (since √(x^6) = x^3)
Therefore, the equivalent expression is 4x^3√2.
Therefore, the correct answer is A. 4x^3√2.