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# How To Calculate The Square Root Of 2? watch

1. I know that cannot be expressed as a fraction due to proof by infinite descent but is there another way to calculate ?

Or is the only method an iterative process of getting closer with each estimate?
2. (Original post by Retsek)
I know that cannot be expressed as a fraction due to proof by infinite descent but is there another way to calculate ?

Or is the only method an iterative process of getting closer with each estimate?
You can do it by using binomial theorem and using lots of terms to make the estimate better and better.
3. You could use the Taylor series of a suitable function. For example,

Or equally . You can cut off this infinite expansion at a point, and get an increasingly accurate approximation for . The more terms you add, the more accurate your approximation. I entered the first 6 or so terms into my calculator and got a pretty accurate estimate within like iirc.

Similarly, you can use the series expansion of to approximate ()
4. (Original post by Retsek)
I know that cannot be expressed as a fraction due to proof by infinite descent but is there another way to calculate ?

Or is the only method an iterative process of getting closer with each estimate?
Press SD on calculator
5. (Original post by Retsek)
I know that cannot be expressed as a fraction due to proof by infinite descent but is there another way to calculate ?

Or is the only method an iterative process of getting closer with each estimate?

https://en.wikipedia.org/wiki/Method...g_square_roots

In addition, you can do this for :

Note that .

Then we can write:

so that

and you can compute the continued fraction as deep as you need for accuracy.

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Updated: October 14, 2017
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