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# Mathematica, <s>17</s> <s>14</s> 13 bytes / <s>12</s> 7 characters

 ⌊#/√2⌋&

[Try it online][1]

-3 bytes because Mathematica accepts the char √, which I copied from [this][2] MathGolf answer.

-1 byte, -5 characters, as per @Mark S. suggestion, by using `⌊⌋`. 

For just one more byte (but 5 more characters) I can always round to the nearest integer with

 Round[#/√2]&

 [1]: https://tio.run/##y00syUjNTSzJTE78n2b7Pyi/NC8lWln/Uccso1i1/wFFmXkl0WnRhgbEgNjY/wA
 [2]: https://codegolf.stackexchange.com/a/198438/75323