Not a Perfect Square

When the number under the root is not a perfect square, do two things: take out the i, then simplify the root as in Algebra. For √(-8), -8 is 8 times -1, so the root is √(8) times i. And 8 is 4 times 2 with 4 a perfect square, so √(8) = 2√(2).

That gives √(-8) = 2√(2)i, with the i written after the closed root. Writing 2√(2i) would put the i under the root, which is a different number. Check by squaring: (2√(2)i)^2 is 4 times 2 times i^2, so -8.

Terms with the same root and an i are like terms, and collect as 2x and x do: √(-8) + √(-2) is 2√(2)i + √(2)i, which is 3√(2)i. When no perfect square divides the number, the root stays as it is: √(-7) = √(7)i.