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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