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?
Just so you know, I used the phrase "happens to be" somewhat ironically. It's easy to prove that it is true for all numbers except zero, starting from the definition. Why do you take this narrow corollary to be more important than the broader definition? But the important thing is this: We can change definitions, but only because doing so produces interesting or useful new mathematics. All you appear to be doing is to remove some mathematics; no one is going to go along with you.
Here we will define, analyze, simplify, and calculate the square root of 0. We start off with the definition and then answer some common questions about the square root of 0.
Then, we will show you different ways of calculating the square root of 0 with and without a computer or calculator. We have a lot of information to share, so let's get started! We call this the square root of 0 in radical form. The square root of 0 is a quantity q that when multiplied by itself will equal 0. As we have calculated further down on this page, the square root of 0 is a whole number. Is the square root of 0 rational or irrational? The square root of 0 is a rational number if 0 is a perfect square.
Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Square root of zero Ask Question. 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.
0コメント