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Methods of computing square roots
There are a numbers of ways to calculate square roots of numbers, and even more ways to estimate them.
The mathematical operation of finding a root is the opposite operation of exponentiation, and therefore involves a similar but reverse thought process.
Firstly, one needs to know how precise the result is expected to be. This is because often square roots are irrational. For example, square root of a nice round whole number 28 is a fraction which in its decimal notation has infinite length, and therefore it is impossible to express it exactly:[math]\sqrt{28} \approx 5.291502622129181....[/math]
Moreover, for some real numbers the square root is a complex number. For example, square root of 4 is a complex number 2i :[math]\sqrt{4} = 2 i[/math]
In many cases there may be multiple valid answers. For example, square root of 4 is 2, but 2 is also a valid answer. One can verify that they are both valid answers by squaring each candidate answer and checking if you obtain 4 as the result of verification:[math]2^2 = 2 \times 2 = 4[/math]
[math](2)^2=(2) \times (2) = 4[/math]
Please note that calculating a square root is a special case of the problem of calculating N^{th} root.
Calculating
Most calculators provide a function for calculation of a square root.
General Steps  Example  

How to calculate a square root using a simple calculator. 


Estimating
If the result does not have to be very precise, the following estimation techniques could be helpful:
Methodology  Example 

Suppose you need to find square root of some number [math]N[/math].
Find some number [math]A[/math] such that [math]A^2[/math] (that is [math]A[/math] squared, or [math]A[/math] times [math]A[/math]) is approximately equal to [math]N[/math] (but how close? This needs to be expanded). Then we can think of [math]A[/math] as being approximately a square root of [math]N[/math]. 
Suppose we need to estimate the square root of 2.
We know that [math]1^2 = 1[/math], and [math]2^2 = 4[/math]. Therefore, one of the answers to [math]\sqrt{2}[/math] is somewhere between 1 and 2. 
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