How to Calculate Square Root Using Continued Fraction

I learned to calculate square root without calculation yesterday. I will explain the method in the next few sentences. For example, I will take the "square root of 2." First, let's define "x=and find the value "a" and "b." "a^2" should be the nearest perfect square number to x, so "a=" because "1^2", which is "1," is the nearest perfect square to "x," which is "2". "b" should be "x-a^2," so "b=1" because "2-1=1". After finding the values of "a", "b," and "x," we can go to the next step, doing continued fraction calculating. The calculation is this, and the more calculation you do, the more the answer will be asymptotic, the true "square root of 2."

The formula of the method:

algebras: "a", "b", "x"

First:

"a^2" is the nearest perfect square to "x"

"b" is "x-a^2"

"x=a^2+b"

Second:

This is the end of the article. I hope you understand what I have said.