## Square Root is not Additive

The square root function is not an additive function.

## Proof

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

$\blacksquare$