The square root of x^2 - 5x + 4 is a real value if x^2 - 5x + 4 >=0

x^2 - 5x + 4 = 0

=> x^2 - 4x - x + 4 =0

=> x(x - 4) - 1(x - 4) = 0

=> (x - 1)(x - 4) = 0

The roots are x = 1 and x = 4

For values of x such that 1< x < 4, x^2 - 5x + 4 < 0

Therefore the square root is defined when

x <= 1 and x >= 4.