What is the equation to convert a square root into a decimal?

Answer 1

There is no simple general method because most square roots are Irrational Numbers. That means their decimal representations are infinitely long. What is required is for you to decide the level of accuracy that you desire. Then use the Newton-Raphson method.

So if you want to find the square root of 56, say,

Define f(x) = x2 - 56

And let f'(x) = 2x

Next, take a starting guess at sqrt(56). You may know that 72 = 49 and 82 = 64 so the answer is going to be between 7 and 8. So start with x0 = 7.

Then iterate: calculate xn+1 = xn + f(xn)/f'(xn) for n = 1, 2, 3, and so on.

Even though x0 is not a particularly good starting point (7.5 would have been better), x3 is accurate to 3 in a billion.