When you take the square root of a positive integer, how many possible answers are there? when you take the cube root of a positive or negative integer, how many possible answers are there?

When you take the square root of a positive integer, there are two possible answers.  Square root is the number you multiply by itself to get your number.  If you're multiplying something by itself, it will either be a negative times a negative or a positive times a positive.  Therefore you must consider both the positive and negative answers.
When you take the cubed root of an integer, there is 1 possible answer.  The cubed root is the number you multiply 3 times to get your number (ex:  the cubed root of 8 is 2, because 2*2*2 = 8).  Since you are multiplying 3 numbers, you could have:
positive * positive * positive = positive
negative * negative * negative = negative
These options don't give you the same sign, so only one of them is correct.

Yes your answer is correct