Square Root Calculator takes a number as input, and finds the square root of given number.
Inputs
Sample inputs
n: 10
n: 620
n: 20500
n: -49
There are several methods to find the square root of a number
The following are some of the most commonly used methods.
Newton's Method: It's an iterative algorithm for finding successively better approximations to the roots (or zeroes) of a real-valued function.
Taylor Series Expansion: Square roots can be computed using Taylor series expansion, where the square root function is approximated using a polynomial expansion around a specific point.
Steps to Find the Square Root using Newton's Method
Follow these steps to find the square root of \(n\).
Start with an initial guess: Choose any positive number '\(a\)' as your initial guess for the square root of n, i.e., \(\sqrt{n}\).
Improve the guess: Use the formula: \(a_{new} = \frac{1}{2}(a + \frac{n}{a})\) to get a new approximation of the square root. This new value \(a_{new}\) is typically closer to the actual square root than the previous guess '\(a\)'.
Repeat until convergence: Keep repeating step 2 with the new value of '\(a\)' until the value of '\(a\)' stops changing significantly (or until you reach a desired level of precision).
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