I'm doing some practice questions for my Complex Numbers unit and I'm confused on how to get the answer for this problem: (Radical -50x^2y^2) My answer guide says that the answer is 5i |xy| (Radical 2) Could someone please show me how to do the problem? Thanks

Answer 1

First, √x^2 is |x| since √ is always positive.
That is, √4 = 2, not ±2
Just because (-2)^2 is also 4 does not mean that -2 is √4

And, since √-50 = √50 √-1 = √25*√2*√-1= 5√2 i
the result is as given: 5i |xy| √2

Answer 2

sqrt(-50x^2y^2) = sqrt(25*2*(-1)x^2y^2) = 5i(xy)sqrt(2).

Note:
sqrt 25 = 5,
sqrt (-1) = i,
2 remains under radical.

Answer 3

Thanks for your help. I understand now and it helped me when solving the other problems in this unit. I appreciate it!!!