Methods of computing square roots
![Graph charting the use of the Babylonian method for approximating the square root of 100 (10) using starting values
x0 = 50,
x0 = 1,
and x0 = −5. Note that using a negative starting value yields the negative root.](/Images/godic/202501/20/Babylonian_method.svg1217.png")
![](/Images/godic/202501/20/Log2approx1218.png")
In numerical analysis, a branch of mathematics, there are several square root algorithms or methods of computing the principal square root of a nonnegative real number. For the square roots of a negative or complex number, see below.
Finding ![\sqrt{S}](/Images/godic/202501/20/1125d8d0ee8e2b14b93166881d6e74b71218.png")
is the same as solving the equation ![f(x) = x^2 - S = 0\,\!](/Images/godic/202501/20/92aae2346fa239ac2f58948b3e2632881218.png")
. Therefore, any general numerical root-finding algorithm can be used. Newton's method, for example, reduces in this case to the so-called Babylonian method: