Question

Which of the following is equal too 8} " alt=" \sqrt{-8} " align="absmiddle" class="latex-formula">
A) 2 $\sqrt{2}$

B) -2 $\sqrt{2}$

C) 2i $\sqrt{2}$

D) 2 $\sqrt{2i}$

Answer 1

You can't have a negative number under a radical that has an even index.  We have an even index since we are dealing with the square root.  Because of that we have to get the imaginary i involved.  $i^2=-1$.  Keeping that in mind, let's rewrite our problem: $\sqrt{(-1)(8)}$.  If -1 equals i-squared, we can sub that in.  Also, since 8 = 4*2 and 4 is a perfect square, let's break that down at the same time: $\sqrt{i^2(4)(2)}$.  i-squared is a perfect square which can be pulled out as a single i, and 4 is a perfect square which can be pulled out as a 2.  We will leave a 2 under the radical.  Here's your simplification: $2i \sqrt{2}$, choice C from above.