Which of the following is equal too √(-8) A) 2 √(2) B) -2 √(2) C) 2i √(2) D) 2 √(2i)

Question

Which of the following is equal too
`√(-8)`

A) 2
`√(2)`

B) -2
`√(2)`

C) 2i
`√(2)`

D) 2
`√(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:
`√((-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:
`√(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 √(2)`, choice C from above.