To solve the equation \( q^2 = 36 \), we take the square root of both sides. Remember that taking the square root gives us both the positive and negative roots.
\[ q = \sqrt{36} \quad \text{or} \quad q = -\sqrt{36} \]
Calculating the square root:
\[ q = 6 \quad \text{or} \quad q = -6 \]
Thus, the solutions are:
\[ q = 6 \quad \text{or} \quad q = -6 \]