Square root

In mathematics, a square root of a number x is another number that, when multiplied by itself (squared), becomes x. When it is not negative, it is represented by the symbol , and called the principal square root of x. For example, 3 is the square root of 9, because 3×3=9. Only numbers bigger than or equal to zero have real square roots. The square root of zero is zero.

An important number is the square root of 2, which is an irrational number. Its value is around 1.41421. It is the length of a diagonal in a square whose side is 1.

Square roots of negative numbers are called imaginary numbers - they are not real numbers. Every complex number, except 0, has two square roots that are imaginary numbers. For example, −1 has two square roots. We call them  and . We also consider the number  as the principal square root of −1, and call it the imaginary unit.

The sign for a square root is made by putting a bent line over a number. For example: . This is read as "the square root of 4".

A whole number with a square root that is also a whole number is called a perfect square. The first few perfect squares are: 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1024, 1089, 1156, 1225.

Below is a table of square roots (rounded to 3 decimal places).
+NumberSquare root of number11.00021.41431.73242.00052.23662.44972.64682.82893.000103.162113.317123.464133.606143.742153.873164.000174.123184.243194.359204.472

 Origin of the symbol 
It is not really known where the square root symbol  comes from, but some people believe that it was from the letter r, which is the first letter of the Latin word radix (used in many languages). Radix means the root or base. Thus, radix quadratum from Latin refers most likely to the base of a square. Since the sides of a square are all equal, the word "radix" may be thought to mean a side of a square.

 Related pages 
 Methods of computing square roots
 nth root

 References 

 Other websites 
 Table of square and square roots, 1-100  -The Math Forum

Category:Mathematics