Question

Why is the answer B? Plz explain.

Answer 1

The original can be rewritten as $\sqrt{-1*6}* \sqrt{-1*24}$.  Because i^2 is equal to -1, we can replace the -1 in each radicand with i^2, like this:  $\sqrt{i^2*6}* \sqrt{i^2*24}$.  Now, i-squared is a perfect square that can be pulled out of each radicand as a single i.  $i \sqrt{6}*i \sqrt{24}$.  24 has a perfect square hidden in it.  4 * 6 = 24 and 4 is a perfect square.  So let's break this up, step by step.  $i \sqrt{6}*i \sqrt{4*6}$  and then  $i \sqrt{6}*2i \sqrt{6}$.  We will now multiply the i and the 2i, and multiply the square root of 6 times the square root of 6:  $2i^2 \sqrt{36}$.  36 itself is a perfect square because 6 * 6 = 36.  So we will do that simplification now.  $2i^2(6)$.  Multiplying the 2 and the 6 gives us $12i^2$.  But here we are back to the fact that i-squared is equal to -1, so 2(-1)(6) = -12.  See how that works?

Answer 2

Remark
Any two (or more than 2) square roots when multiplied together can be put under 1 square sign. 

In this case sqrt(-6)*sqrt(-24) can be put under 1 square root sign. 

sqrt( -6 * - 24) = sqrt(+144) = 12
For this question you do not need to solve the complex numbers.