Which numbers are equal to their squares?

Answer 1

One 0 and 1 0 X 0 = 0 1 X 1 = 1

Only positive 1 though.

Negative 1 will produce the answer of a positive 1.

Solve x = x^2
x^2 - x = 0
x ( x - 1 ) = 0
Has solutions x=0 and x=1

Answer 2

The numbers that are equal to their squares are 0 and 1. When you square 0, you get 0. When you square 1, you also get 1. These are the only two numbers that satisfy this property. All other numbers have a square that is greater than the original number.