Simplify sqrt(-8)times sqrt(-12))
A. 4 times sqrt(6)
B. -4i times sqrt (6)
C. 4i times sqrt(6)
D. -4 times sqrt (6)
To simplify the expression sqrt(-8) times sqrt(-12), you need to evaluate the square roots separately and then multiply the results.
Step 1: Simplify the square roots individually.
sqrt(-8) = sqrt(8) * i = 2 * sqrt(2) * i
Here, we have used the property that sqrt(-1) = i.
sqrt(-12) = sqrt(4 * 3) * i = 2 * sqrt(3) * i
Step 2: Multiply the simplified square roots.
(2 * sqrt(2) * i) * (2 * sqrt(3) * i)
= 4 * sqrt(2) * sqrt(3) * i^2
Since i^2 = -1, we can simplify further:
= 4 * sqrt(2) * sqrt(3) * -1
= -4 * sqrt(6)
Therefore, the simplified expression sqrt(-8) times sqrt(-12) is equal to -4 times sqrt(6).
Hence, the correct answer is option D: -4 times sqrt(6).