What number or numbers are equal to their own square roots?

The numbers that are equal to their own square roots are 0 and 1. This is because if ( x ) is a number, then ( x = \sqrt{x} ) leads to the equations ( x^2 = x ). Solving this gives ( x(x - 1) = 0 ), resulting in the solutions ( x = 0 ) and ( x = 1 ).