First, you must factor a -1 from the number. -50 = -1 * 50. Then you separate the roots into the product of roots. The square root of -1 is i.
[tex] \sqrt{-50} = \sqrt{-1 \times 50} = \sqrt{-1} \times \sqrt{50} = i\sqrt{50} [/tex]
So far we took care of the negative root. Now you need to simplify the square root of 50. Since you are dealing with a square root, you need to find the largest perfect square integer that is a factor of 50. It happens to be 25. 25 is a perfect square integer since it is the square of 5, and 25 is the largest perfect square integer factor of 50 since 2 * 25 = 50. Now we factor 50 into 25 * 2, we separate the roots, and take out the root of 25.
[tex] i\sqrt{50} = i\sqrt{25 \times 2} = i\sqrt{25} \times \sqrt{2} = i \times 5 \times \sqrt{2} = 5i\sqrt{2} [/tex]
