Add √2 + √3 = 3.14626437

BehindTheScenes

Does anyone know how to do the steps in the above problem without a calculator? Your help is really appreciated, all I can find on the net is that it can't be solved, although my calculator says differently!:pac::pac:

biko

= √2 + √3
= 1.414214 + 1.732051
= 3.146264

or do you mean how to calculate the √2 ?
http://www.homeschoolmath.net/teaching/square-root-algorithm.php

BehindTheScenes

biko wrote: »

= √2 + √3
= 1.414214 + 1.732051
= 3.146264

or do you mean how to calculate the √2 ?
http://www.homeschoolmath.net/teaching/square-root-algorithm.php

Hey Biko,

I'm looking for the steps to calculate √2 and√3 to decimal numbers. Tried calculating it but Jesus I'm struggling.

764dak

BehindTheScenes wrote: »

Hey Biko,

I'm looking for the steps to calculate √2 and√3 to decimal numbers. Tried calculating it but Jesus I'm struggling.

If you know a little calculus you can use the Newton-Raphson method.



You have to repeat the process until you have an accurate enough number

If x = √2 then x^2 = 2.
f(x) = x^2 - 2 and f'(x) = 2x
You have to guess a value for the original x that is close to the value you think it is. I'll use x = 1.4 as the initial value.

x = 1.4 - f(1.4)/f'(1.4) = 1.4 -(-0.04)/(2.8) = 1.41428571
x = 1.41428571 - f(1.41428571)/f'(1.41428571) =

http://en.wikipedia.org/wiki/Newton%27s_method#Square_root_of_a_number

There are actually other ways as well: http://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Digit-by-digit_calculation

BehindTheScenes

764dak wrote: »

If you know a little calculus you can use the Newton-Raphson method.



You have to repeat the process until you have an accurate enough number

If x = √2 then x^2 = 2.
f(x) = x^2 - 2 and f'(x) = 2x
You have to guess a value for the original x that is close to the value you think it is. I'll use x = 1.4 as the initial value.

x = 1.4 - f(1.4)/f'(1.4) = 1.4 -(-0.04)/(2.8) = 1.41428571
x = 1.41428571 - f(1.41428571)/f'(1.41428571) =

http://en.wikipedia.org/wiki/Newton%27s_method#Square_root_of_a_number

There are actually other ways as well: http://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Digit-by-digit_calculation

Thanks, looked through the link provided and I just wanted to ask is it possible to solve the equation using differentaition?

Iderown

Is there any scheme that could be developed using the fact that
(√3 + √2)(√3 - √2) = 1

764dak

BehindTheScenes wrote: »

Thanks, looked through the link provided and I just wanted to ask is it possible to solve the equation using differentaition?

Here is a way using differentiation although the answers sometimes aren't really accurate: http://dominicmary.blogspot.com/2012/06/finding-square-root-of-integer-using.html and http://www.math-prof.com/Calculus_1/Calc_Ch_23.asp.

Here is a way using Taylor Series:

http://www.understandingcalculus.com/chapters/23/23-1.php

FoxT

Iderown wrote: »

Is there any scheme that could be developed using the fact that
(√3 + √2)(√3 - √2) = 1

That's an interesting insight - but on the face of it I don't think so because

(√(n+1) + √(n))(√(n+1) - √(n)) = (n+1)-(n) will always be = 1.

ie - (√3 + √2)(√3 - √2) = 1 is not unique.