• Question: what is the square root of -0 (this broke my calculator)

    Asked by yurt534dote63 on 27 Oct 2025.
    • Photo: Amy Mason

      Amy Mason answered on 27 Oct 2025:

      That is because you are smarter than your calculator and can work out things it can’t.

      So we need a couple of piece of information to solve this.
      First 0x0 is 0 – so the square root of 0 is 0.

      Second, the square root of -a is i times the square root of a. Here i is the square root of -1, an imaginary number – if you don’t know about them, you should read or watch something about them.

      So the square root of -0 is i x 0 – but anything times 0 is 0, so that answer is 0.

    • Photo: Caroline Roche

      Caroline Roche answered on 10 Dec 2025:

      0 is a special number, in that neither -0 nor +0 exist, there is only 0.
      But your calculator doesn’t see it that way, just that there is a negative number and it knows not to square root negative numbers because then it needs imaginary numbers which are too complicated for it to handle, so it brings up an error.
      You can get smarter calculators or computer programs to help handle the more complicated maths.

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