√(<em>x</em> + 1) + 3 = 0 ==> √(<em>x</em> + 1) = -3
has no real solutions, since the square root cannot be a negative number. But if we were to ignore that for the moment, one might try taking the square of both sides, which gives
(√(<em>x</em> + 1))² = (-3)² ==> <em>x</em> + 1 = 9 ==> <em>x</em> = 8
But this is not a valid solution, since
√(8 + 1) = √9 = 3 ≠ -3
While -3 is a square root of 9, we had started off with the *positive* square root of <em>x</em> + 1.
