Babylonian clay tablet YBC 7289 (c. 1800–1600 BC) with annotations. The approximation of the square root of 2 is four sexagesimal figures, which is about six decimal figures. 1 + 24/60 + 51/60² + 10/60³ = 1.41421296...

Numerical analysis studies different algorithms to get approximations for problems of mathematical analysis. Approximations are used for the following reasons:

1. There are no known ways to solve a problem using calculus. Examples for such problems are the Navier–Stokes equations or the Three-body problem
2. There is a way to solve a problem using calculus. Getting an exact solution is impractical though, because it requires a long time, or many resources. An example for this is calculating Power series.

One of the earliest known uses of numerical analysis is a Babylonian clay tablet, which approximates the square root of 2. In a unit square, the diagonal has this length. Being able to compute the sides of a triangle is extremely important, for instance, in carpentry and construction.