Question

When approximating the square root of 2 by applying Newton's Method, is the answer (+-)1.4142 or just positive 1.4142?

Answer 1

generally Newton's method will give you one of the roots, but the other one is the negative of the one found.

Answer 2

I would define this function: f(x) = x²-2.
Differentiating gives f'(x) = 2x.
Newtons method:\[x _{n+1}=\frac{ x _{n}^{2}+2 }{ 2x _{n} }\]

Starting with a positive number for x0, will lead you to 1.4142...
A negative start value goes to -1.4142...

See attached img

Answer 3

Ok, so (+-)1.4142 is a suitable answer to the problem

Answer 4

Yes, it is.