Sam's Mistake

Algebra Level 4

Sam is excited to learn about the distributive law, and thinks that it applies to every possible operation. As such, he claims that \[\sqrt{a^2 + b^2} = \sqrt{a^2} + \sqrt{b^2}\]

How many ordered pairs of integers \((a, b\)) are there, such that \(-10≤a≤10, -10≤b≤10\) and \[\sqrt{a^2 + b^2} = \sqrt{a^2} + \sqrt{b^2}?\]

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