did you mean  sqrt (a^2 + b^2)  not =  a + b ??

there are an infinite number of examples

    a= 1 .. b = 2

   sqrt(1 + 4)  not = 1 + 2

    sqrt5  not = 3

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or  a = 2, b = 3

   sqrt(4 + 9)  not = 2 + 3

   sqrt(13)  not = 5

Let a = 4 and b = 3

a^2 will be 16 and b^2 will be 9;

√(16 + 9) = √25 = 5 but 4 + 3 = 7