About Decatur
Decatur Artist
Decatur Art Galleries
Youtube Videos
Decatur Happenings
 Art Events
 Singles
 Nonprofit
 Dance
Decatur Georgia
Pictures
Homes for Sale
Home Page
Decatur Businesses
 Eating
 Lodging
 Services
 Shopping
Community Info
 Healthcare
 Neighborhoods
 Nonprofits
 Pets
 Religion
 Schools
 Transportation
Entertainment
Events Calendar
Local Links
  

Abstract Photography Downtown DecaturIn mathematics, a square root of a number x is a number r such that r2 = x, or in words, a number r whose square (the result of multiplying the number by itself) is x. Every nonnegative real number x has a unique nonnegative square root, called the principal square root and denoted with a radical symbol as \sqrt x. For example, the principal square root of 9 is 3, denoted \sqrt 9 = 3, because 3^2 = 3\times3 = 9. The other square root of 9 is 3.

Square roots often arise when solving quadratic equations, or equations of the form ax2 + bx + c = 0, due to the variable x being squared.

Every positive number x has two square roots. One of them is \sqrt{x}, which is positive, and the other is \sqrt{x}, which is negative. Together, these two roots are denoted \pm\sqrt{x}. Square roots of negative numbers can be discussed within the framework of complex numbers. Square roots of objects other than numbers can also be defined.

Square roots of integers that are not perfect squares are always irrational numbers: numbers not expressible as a ratio of two integers. For example, \sqrt 2 cannot be written exactly as \ m/n, where n and m are integers. Nonetheless, it is exactly the length of the diagonal of a square with side length 1. This has been known since ancient times, with the discovery that \sqrt 2 is irrational attributed to Hipparchus, a disciple of Pythagoras. (See square root of 2 for proofs of the irrationality of this number.)


  