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

a2+b2=a2+b2. \sqrt{a^2+b^2} = \sqrt{a^2} + \sqrt{b^2} .

How many ordered pairs of integers (a,b) (a, b) are there, such that 10a10,10b10 -10 \leq a \leq 10, -10 \leq b \leq 10 and

a2+b2=a2+b2? \sqrt{ a^2 + b^2} = \sqrt{a^2} + \sqrt{b^2} ?


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