If square root of n equals to 3/2 what is - square root of n

 C) 5

Work Shown:

s = square side length

A = area of square = 9x^2+12x+4

A = s^2

A = (ax+b)^2

A = a^2*x^2 + 2abx + b^2 apply the FOIL rule

A = 9x^2 + 12x + 4

Equating corresponding terms, we see that,

a^2*x^2 = 9x^2 which shows that a^2 = 9 and that solves to a = 3, assuming 'a' is positive.2abx = 12x leads to 2ab = 12 or ab = 6. Using a = 3 we can find that b = 2.b^2 = 4 solves to b = 2 which matches with the previous value of b found.

Using a = 3 and b = 2, the sum of the values is a+b = 3+2 = 5, so that's why the answer is choice C.

Side note: 9x^2 + 12x + 4 factors to (3x + 2)^2