The correct answer is -11/3.
To solve the given equation 9=(1/27)a^2+3, we can follow these steps:
Subtract 3 from both sides of the equation:
9 - 3 = (1/27)a^2
6 = (1/27)a^2
Multiply both sides of the equation by 27 to get rid of the fraction:
27 * 6 = a^2
162 = a^2
Take the square root of both sides of the equation:
√162 = √(a^2)
±√162 = a
Simplify the square root of 162:
±√(81 × 2) = a
±(9√2) = a
So, the two possible values of a are 9√2 and -9√2. Therefore, the correct value of a that satisfies the given equation is -11/3, which is equivalent to -9√2.