To solve the equation \( a^2 = 225 \), we can take the square root of both sides:
\[ a = \pm \sqrt{225} \]
Calculating the square root, we find:
\[ \sqrt{225} = 15 \]
Thus, the solutions for \( a \) are:
\[ a = 15 \quad \text{and} \quad a = -15 \]
Therefore, the complete solution set for \( a \) is:
\[ a = \pm 15 \]
Among the provided choices, the correct answer is:
\[ \text{a = ±15} \]