The square root of a number is the value of one of two equal factors of that number. For example, the number 16 has the factor 4, which when multiplied by itself (ie: 4*4) gives 16. Hence the square root of 16 is 4. Minus 4 (-4) is also a square root of 16, as it gives sixteen when multiplied by itself.
The square root can also be shown to be the 1/2 power of the number.
The square root function generally maps rational numbers to algebraic and constructible irrational numbers, except in cases where the numerator and denominator are both perfect squares. It also maps the area of a square to its side length.
Rapidly convergent methods for calculating rational approximations of irrational square roots include Newton's method and Pell's equation.