You have the function:
f(x) = 5√x - 1
the average rate of change for the interval x=3 to x = 4.5 is:
m = (f(4.5) - f(3))/(4.5 -3)
f(4.5) = 5√(4.5) - 1 = 9.60
f(3) = 5√(3) - 1 = 7.66
m = (9.60 - 7.66)/(4.5 - 3)
m = 1.93/1.5
m = 1.3
The rate of change is 1.3