Find the two expression that are equivalent to 3√-125, -3√125, I-5I?

Answer 1

1st:
3sqrt -125
3i sqrt 25 * 5
=15i sqrt 5

2nd:
-3 sqrt 125
-3 sqrt 25 * 5
-15 sqrt 5

Answer 2

cube root of a negative number is a negative number and cube root of a positive number is positive only.

the first expression works out to -5 because:
-5 * -5 * -5 = +25 * -5 = -125

the second expr: is negative of cube root of positive 125. the cube root is +5, and negative of that is -5.

So 1 and 2 are equivalent.

The third expression | something| is not negative by definition; in fact it is +5, so it is not the same.