The square root of a negative number involving imaginary units.?

Question

Ok I need to figure out how to get to the square root of -11 however not simply as √11i. For example.
√-18 = √9 X √2 X √-1 or 3√2i so the final answer to √-18 in imaginary numbers as a whole would be 3√2i

I understand the process but I cannot remember how to get to the answer for
√-11

Answer 1

the first thing to remember is that: i = √-1
since you can't have a negitive under the square root sign, it makes it an imaginary number which you can then take out:
√-11 =
√11 * (√-1 or i)
therefore the answer would be i√11

(11 cannot be broken down any further because it does not factor; that's why it might have looked different than your prior example)

hope i helped.

Answer 2

In this case it is √11i because there is nothing you can factor out of 11 that is a perfect square. In the the example you provided of √-18, you could factor the perfect square 9 out of -18 in order to simplify, but with √-11 there is no perfect square to factor out. So it is just √11i.

Answer 3

√-11 =
√11 * √-1 =
√11 * i or
i√11

Answer 4

well in this case is would be i*sqrt(11) because 11 is prime and has no factors