Is it possible to square root zero

You should upgrade or use an alternative browser. Square Root of Zero. Thread starter Mr. Bland Start date Jan 13, Bland Junior Member. Joined Dec 27, Messages This thread got me thinking about something I've had in the back of my mind for a while I'm not completely sold on that idea. It's a narrow, incomplete view of square root, and the claim doesn't hold up under broader scrutiny Far be it from me to be the guy who says that "literally all mathematicians everywhere" are wrong about the square root of zero, so I figure there's something else at play that isn't obvious.

Are there some special circumstances surrounding the square root of zero that don't apply to non-zero numbers? Is it something that's context-dependent? Romsek Senior Member.

Joined Nov 16, Messages 1, Your proposition falls apart at your first statement. It never makes mathematical sense to talk about dividing by zero because that operation is undefined. Further the square root of negative numbers is undefined on the reals.

Peterson Elite Member. Joined Nov 12, Messages 12, That's just a matter of definition. Now, the rest of what you say is based not on a definition , but about a fact that happens to be true for non-zero numbers, but which you have not proved to be necessarily true for all non-negative numbers x. What you are doing is ignoring conditions in your statements, and therefore deriving contradictions.

Cubist Senior Member. Joined Oct 29, Messages 1, Romsek said:. Click to expand Peterson said:. Now, the rest of what you say is based not on a definition , but about a fact that happens to be true for non-zero numbers [ Bland said:. From my perspective, square root works the way it does regardless of how humans choose to articulate it , a fact that was instrumental in the discovery of complex arithmetic.

There was a time for those who don't know the story when it was considered a non-operation to take the square root of a negative number.

Under that definition, it was impossible to solve certain cubics because square roots of negative numbers turned up during the algebra. So the "nonsensical" operation was investigated, and since that time, we've learned more about the nature of arithmetic and are now able to solve all forms of cubics as a result.

We learned about square root because we studied it, not because we defined it. If we say that square root is, exactly, "the value that when squared gives the input" plus or minus a plus-or-minus , then sure, zero is its own square root. However, from a practical sense, where we work with discrete operations and study their relationships, we encounter situations where square root is meaningful yet not fitting within that definition. When accounting for complex and higher-order arithmetic, unless I'm terribly mistaken which might be the case , dividing a number by one of its square root s gives one of its square root s for all values except zero, because division by zero is undefined.

This notion is analogous to how you can't use division to "undo" a multiplication by zero, which to me is sensible considering square root's relation to division.

And from my perspective, this makes it look as though the square root of zero is undefined. Thanks for bearing with me. I understand that I may not be adequately expressing what's in my head, and I'm grateful for your patience.

Are you claiming that the concept of square root is broader than the definition, or narrower? What situation do you have in mind that doesn't fit the accepted definition? What new definition would you offer? Why would the fact that you can't divide by zero invalidate the square root?

So you're narrowing the definition, by excluding one value, namely zero. Why do you say you are broadening it??? So what, in your opinion, is the "correct" definition?

And how does "correcting" it improve mathematics? Asked 2 years, 10 months ago. Active 4 months ago. Viewed 2k times. Jessica Jessica 39 2 2 bronze badges. It is a result rather than a definition. Add a comment. Active Oldest Votes. Matt Samuel Matt Samuel Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password.

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