Additive Function (Conventional)/Examples/Square Root is not Additive

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Square Root is not Additive

The square root function is not an additive function.


Proof

Proof by Counterexample:

\(\displaystyle \sqrt 9\) \(=\) \(\displaystyle 3\)
\(\displaystyle \sqrt {16}\) \(=\) \(\displaystyle 4\)
\(\displaystyle \sqrt {9 + 16}\) \(=\) \(\displaystyle \sqrt {25}\)
\(\displaystyle \) \(=\) \(\displaystyle 5\)
\(\displaystyle \) \(\ne\) \(\displaystyle 3 + 4\)
\(\displaystyle \) \(=\) \(\displaystyle \sqrt 9 + \sqrt {16}\)

$\blacksquare$


Sources