Quotient Rule Word Problem

I am having difficulty remembering how to multiply the square root portion of this problem.

A study indicates that spending money on pollution control is effective up to a point but eventually becomes wasteful. Suppose it is known that when x million dollars is spent on controlling pollution, the percentage of pollution removed is given by:

P(x) = 100(square root x)/0.03x^2+9

Determine the expenditure that results in the largest percentage of pollution removal. What is this maximum percentage?

According to the quotient rule, I have (0.3x^2+9)(100square root x)-(100square root x)(0.06x)/(0.03x^2+9)^2

Multipling out (3x+900square root x)-(6x^3/2)/0.03x^2+9)

If I am right so far, can you give me a nudge on what to do with all these square roots?

Thank You