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Through the binomial expansion of $(1 - 2x)^\frac{1}{2}$, I am required to find an approximation of $\sqrt2$. Binomial expansion $ (1 + x)^n = 1 + \frac{n}{1}x + \frac{n(n-1)}{1*2}x^2 + .....
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Approximating square roots using binomial expansion. Jul 24,...
- Binomial expansion of square root
Is the binomial expansion a good method to find the...
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Free Binomial Expansion Calculator - Expand binomials using the binomial expansion method step-by-step.
The binomial approximation for the square root, + + /, can be applied for the following expression, 1 a + b − 1 a − b {\displaystyle {\frac {1}{\sqrt {a+b}}}-{\frac {1}{\sqrt {a-b}}}} where a {\displaystyle a} and b {\displaystyle b} are real but a ≫ b {\displaystyle a\gg b} .
1 lip 2017 · Is the binomial expansion a good method to find the approximate value of the square root to second order in $x$? If yes, how should I binomial expand it? $a$ could be a negative number or an imaginary number or a positive number.
6 mar 2023 · You can check that that is an approximation of root 2 by calculating its square. If you want you know why this works, you could start with https://en.wikipedia.org/wiki/Binomial_approximation, particularly the generalisation near the end.
13 wrz 2023 · How do I use a binomial expansion to approximate a value? Ignoring higher powers of x leads to an approximation; The more terms the closer the approximation is to the true value; For most purposes, squared or cubed terms are accurate enough
By strategically choosing 'a' and 'b', we can use the binomial expansion to approximate square roots and other roots. While the binomial expansion doesn't give us exact answers for roots, it offers a valuable tool for quick approximations.
