Question

Which expression is equal to 2√ -28?

4i√7


−4i√7


4√7i


−4√7
I found the answer it's 4i√7

Answer 1

`4i √(7)`

Explanation:

To figure this out, you need to find two numbers where one of them is a non-perfect square and the other is. In this case, you have to add the iota symbol in there since we are dealing with the square root of a negative. This is how you do it:

`2√( -28) \\ 2 √((i)(7)(4)) \\ (2)2i √(7) = 4i √(7)`

So, what happened here was that after finding our two numbers, including iota in this case, I took the square root of 4 since it is a perfect square, and brought it to the outside right up against the other 2, making 2 × 2 equal 4. Now, keep in mind that whenever you are dealing with the Complex Number System, you also have to bring the iota symbol to the outside as well, or else you will have this:

`4i√(-7) \\ and \\ 4i√(7) ≠ 4i √(-7)`

This leaves the 7 inside the radical, since it is a non-perfect square.

Extended information on Complex Numbers

√-1 = i

-1 = i²

-i = i³

1 = i⁴

I am joyous to assist you anytime. -_-