To solve the equation \( p^2 - 36 = 0 \), we can first isolate the \( p^2 \) term:
\[ p^2 = 36 \]
Next, we take the square root of both sides:
\[ p = \pm \sqrt{36} \]
Calculating the square root, we get:
\[ p = \pm 6 \]
Thus, the solutions are:
\[ p = 6 \quad \text{or} \quad p = -6 \]
So the final answers are:
\[ p = 6 \quad \text{or} \quad p = -6 \]