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
\(\ds \sqrt 9\) | \(=\) | \(\ds 3\) | ||||||||||||
\(\ds \sqrt {16}\) | \(=\) | \(\ds 4\) | ||||||||||||
\(\ds \sqrt {9 + 16}\) | \(=\) | \(\ds \sqrt {25}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 5\) | ||||||||||||
\(\ds \) | \(\ne\) | \(\ds 3 + 4\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \sqrt 9 + \sqrt {16}\) |
$\blacksquare$
Sources
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): additive function