# Poor Man's Euclidean Norm

Calculus Level 4

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?

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