Question

Approximation

Answer 1

How\[\sqrt {1-\frac{x^2+y^2}{a^2}}\approx(1-\frac{x^2+y^2}{2a^2})\]?

Answer 2

Ever hear of a Binomial Expansion?

Answer 3

ofc. I can show that using binomial theorem?

Answer 4

Yup. The next term would be \(-\dfrac{1}{8}\left(\dfrac{x^{2}+y^{2}}{a^{2}}\right)^{2}\), so the approximation is a little high.

Answer 5

I don't need to show it, I just need to know how can I show it. So, the answer is using binomial theorem?

Answer 6

Yes, that will do. It is using the Binomial Theorem up to the Linear Term and discarding all higher-order terms.

Answer 7

Thanks