For how many real values of x is sqrt(120 - sqrt(x)) an integer?

Solve for x:

sqrt(120 - sqrt(x)) = 0

Square both sides:

120 - sqrt(x) = 0

Subtract 120 from both sides:

-sqrt(x) = -120

Multiply both sides by -1:

sqrt(x) = 120

Raise both sides to the power of two:

x = 14,400