4
$\begingroup$

I know this is a dumb question but I can't get the answer to another follow up question,

  1. What is the square root of 1?
  2. If the square root of 1 is itself then why does other square root of number not equal to themselves?
  3. Is there other square root of 1 aside from 1?

This question is somewhat a deconstruction of the fundamental logic of mathematical concepts but I can't find a good reason to answer this questions. Hoping for a good reason.

[Edit] if we're going to talk about principal square roots then therefore -1 would be included but i'm only referring to non negative numbers therefore 3.1. if there are other square root of 1 which could be between 0 and 1?

  • 7
    no one has mentioned that $0 \cdot 0 = 0$. This can be attained from the equation $x^2=x \implies x(x-1)=0 \implies x=0 \, \mathrm{ or } \, 1$2011-04-14
  • 0
    The square of a positive number less than 1 is less than itself: $0\lt x\lt 1$ implies $0\lt x^2\lt x$ (multiplying through by $x$); so no number between $0$ and $1$ can be the square root of a larger number (in particular, of $1$).2011-04-14
  • 0
    @sergiol No it doesn't: $-1^2=1\not=-1$. What you might be confused by: $-1$ *does* satisfy $x^2=\sqrt{x^2}$, but that's because square roots don't work the way they "should."2015-05-21

3 Answers 3