Poor Man's Euclidean Norm

Suppose you have two numbers, $A$ and $B$ , where $A > B > 0$ . The expression for the Euclidean norm of these two numbers is shown below:

Euclidean norm = $\sqrt{A^{2}+B^{2}}$

Suppose we would like to approximate this using an even simpler expression, as shown below:

Approximate Euclidean norm = $A+$ $\frac{1}{2}$ $B$

What is the maximum percentage error that this approximation can introduce?