Let f(n) = 2 (log n)² + 5n² log n+ square root of n

Please give all the details for the below statements (i.e. give the witnesses C and k).

a. (5 points) Show that f(n) is not O(square root of n ).

b. (5 points) Show that f(n) is O(n³)^.

c. (5 points) Show that f(n) is (log n).

d. (5 points) Show that f(n) is (n² log n ).