Square root

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A square root of a number is a number that, when it is multiplied by itself (squared), gives the first number again. For example, 2 is the square root of 4, because 2×2=4. Only numbers bigger than or equal to zero have real square roots. A number bigger than zero has two square roots: one is positive (bigger than zero) and the other is negative (smaller than zero). For example, 4 has two square roots: 2 and −2. The only square root of zero is zero.

Square roots of negative numbers are not real numbers – they are imaginary numbers. Every complex number except 0 has 2 square roots. For example: −1 has two square roots. We call them i and -i.

The sign for a square root is made by putting a bent line over a number, like this: \sqrt 4. We say "the square root of 4" (or whatever number we are taking the square root of).

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...

Symbol[change | edit source]

It is not really known where the square root symbol \sqrt{\,\,} comes from, but some people believe that it was from the letter r, which is the first letter of the Latin and German word radix. Radix means square root.