Difference between revisions of "Root (operation)"
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==Definition== | ==Definition== | ||
| − | For any (not necessarily real) numbers <math>x,y,n</math>, <math>y=\sqrt[n]{x}</math> if <math>y^n | + | For any (not necessarily real) numbers <math>x,y,n</math>, <math>y=\sqrt[n]{x}</math> if <math>y^n=x</math>. Note that we generally take only the positive value of <math>y</math>, if we wish to take both the positive and negative roots, we write <math>\pm\sqrt[n]{x}</math>. |
==See Also== | ==See Also== | ||
Revision as of 16:31, 28 October 2012
The 
th root of a number 
, denoted by ![$\sqrt[n]{x}$](http://latex.artofproblemsolving.com/0/2/d/02d35112ae0400463779b8c3320f3bc597d81374.png)
, is a common operation on numbers and a partial inverse to exponentiation. (The proper inverse is the logarithm)
Definition
For any (not necessarily real) numbers 
, ![$y=\sqrt[n]{x}$](http://latex.artofproblemsolving.com/9/9/6/9962081cf8b6e34039528449be2773a54b04cf8d.png)
if 
. Note that we generally take only the positive value of 
, if we wish to take both the positive and negative roots, we write ![$\pm\sqrt[n]{x}$](http://latex.artofproblemsolving.com/6/6/3/663f9e8b75a5e424090d648fb042a266557b4538.png)
.
See Also
- Algebra
- Square root, a special form of a root.
