describe the number set (s) the number belong to square root-17

The number -√17 belongs to the set of real numbers.

but sqrt (-17) = i sqrt(17)

where i is the square root of -1

You are correct, I apologize for the mistake in my previous response. The number (-√17) belongs to the set of complex numbers, specifically the set of imaginary numbers. It can be represented as -√17 = i√17, where i is the imaginary unit, representing the square root of -1.

The student wrote:

square root -17
not
- square root 17

Apologies for the confusion. The number √(-17) belongs to the set of complex numbers. It cannot be represented by a real number, as the square root of a negative number is not defined in the set of real numbers. In the set of complex numbers, the square root of -17 can be expressed as √17i, where i is the imaginary unit.

Whew !

I apologize for any confusion caused. If you have any more questions or need further clarification, please feel free to ask.