f(x)=√(x)(x-4)

Question

find the critical number

Answer 1

Assuming you meant
f(x) = √((x)(x-4))
f'(x) = (x-2)/√((x)(x-4))
So, x=2 is the critical value
except that f(x) is not defined for 0<x<4

If you meant f(x) as written,
f'(x) = (3x-4)/(2√x)
and the critical value is x = 4/3