Radical mistake

Algebra Level 3

Sherry is excited to learn about the distributive law, and thinks that it applies to every possible operation. As such, she 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 \( -10 \leq a \leq 10, -10 \leq b \leq 10 \) and

\[ \sqrt{ a^2 + b^2} = \sqrt{a^2} + \sqrt{b^2} ?\]

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