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root value

How to caluclate root of 2

Note by Sai Venkata Raju Nanduri
4 years, 3 months ago

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We can use this method to calculate the root of 2 or any other non-square integer.

http://en.wikipedia.org/wiki/Methodsofcomputingsquareroots

After 5 steps computing using the CASIO fx-500MS calculator, I got \[ \sqrt{2} \approx 1.414213562 \] Đức Việt Lê · 4 years, 3 months ago

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@Đức Việt Lê u are correct Vamsi Krishna Appili · 4 years, 3 months ago

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however if you know the basic of number theory and if you know the theorem of "continued infinite fractions" then you could find square root of any integer as a form of continued fraction tending to infinity.... Raja Metronetizen · 4 years, 3 months ago

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One method I learned was use the binomial theorem. (1+1)^(1/2) Harrison Lian · 4 years, 3 months ago

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@Harrison Lian Yes very good Justin Wong · 4 years, 3 months ago

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@Harrison Lian But, how can you calculate 2^(1/2)? I didn't know about that method. Can you tell me please? Đức Việt Lê · 4 years, 3 months ago

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@Đức Việt Lê \(2^{\frac {1}{2}}\) is the same as \(\sqrt[2]{2}\), which is the same as \(\sqrt 2\). Infact, \(\sqrt[n]{x}\) is the same as \(x^{\frac {1}{n}}\). Shourya Pandey · 4 years, 3 months ago

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@Shourya Pandey Yes I knew it before I post. But are there any other methods to calculate a power of \[ \frac{1}{n} \] with n integer? Đức Việt Lê · 4 years, 3 months ago

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@Đức Việt Lê ask google Vamsi Krishna Appili · 4 years, 3 months ago

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One of my favorite ways is to solve the diophantine equation x^2-2y^2=1 for positive integers x and y. The larger the integers, the better x/y approximates the square root of 2. You can find solutions using Brahmagupta's chakravala (cyclic) method, which is an elegant algorithm for finding solutions to Pell equations. Jason Martin · 4 years, 3 months ago

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read NCERT of class 8 chapter 6 Neeraj Kadian · 4 years, 3 months ago

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read NCERT of class 8 chapter 6 Genious Boy · 4 years, 3 months ago

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around 1.414 Tan Li Xuan · 4 years, 3 months ago

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by using taylor - macloren method Ahmed Magdy · 4 years, 3 months ago

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take a calculator.the type like this (2)^1/2.then press "=".you will get the answer. Sreehari Vp · 4 years, 3 months ago

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Le V is correct....

its 1.414 Vamsi Krishna Appili · 4 years, 3 months ago

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Comment deleted May 12, 2013

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@Shourya Pandey You can use long division method:

http://www.ask-math.com/square-root-by-long-division-method.html

http://nrich.maths.org/5955

http://www.gurubix.com/video-295-HowtofindsquarerootofanumberLongdivisionmethodSquaresandsquareroots

Check these. Hope it helps! Shourya Pandey · 4 years, 3 months ago

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you are 17...so well by ur standard, Let x be the nearest perefct square near it, i.e. 1... f(x) = x, i.e. 1; so f'(x) = nx^(n-1) putting n=1/2, f'(x) = (x^(-1/2))/2 = 1/(sqrt{1}) now f(x+delta(x)) = f(x) + f'(x)delta(x) = 1 + 1/21 = 1 + .5 = 1.5(approx) but to find the actual value, use the division method as u did in the earlier classes VII or VIII but for the larger no. such as 345 or 234, this method is quite awesome... Shubham Sharma · 4 years, 3 months ago

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Use scientific calculator. Gil Deon Basa · 4 years, 3 months ago

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