To solve the equation \( v^2 - 52 = 48 \), we first isolate \( v^2 \):
\[ v^2 - 52 = 48 \]
Adding 52 to both sides, we get:
\[ v^2 = 48 + 52 \]
\[ v^2 = 100 \]
Next, we take the square root of both sides:
\[ v = \sqrt{100} \quad \text{or} \quad v = -\sqrt{100} \]
Calculating the square root:
\[ v = 10 \quad \text{or} \quad v = -10 \]
Thus, the solutions are:
\[ \boxed{10} \quad \text{or} \quad \boxed{-10} \]