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

Square Root is not Additive

The square root function is not an additive function.

Proof

Proof by Counterexample:

\(\ds \sqrt 9\)

\(=\)

\(\ds 3\)

\(\ds \sqrt {16}\)

\(=\)

\(\ds 4\)

\(\ds \sqrt {9 + 16}\)

\(=\)

\(\ds \sqrt {25}\)

\(\ds \)

\(=\)

\(\ds 5\)

\(\ds \)

\(\ne\)

\(\ds 3 + 4\)

\(\ds \)

\(=\)

\(\ds \sqrt 9 + \sqrt {16}\)

$\blacksquare$

Sources

• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): additive function