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....

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.

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...

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## Comments

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

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

ofcomputingsquarerootsAfter 5 steps computing using the CASIO fx-500MS calculator, I got \[ \sqrt{2} \approx 1.414213562 \]

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u are correct

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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....

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One method I learned was use the binomial theorem. (1+1)^(1/2)

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Yes very good

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But, how can you calculate 2^(1/2)? I didn't know about that method. Can you tell me please?

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\(2^{\frac {1}{2}}\) is the same as \(\sqrt[2]{2}\), which is the same as \(\sqrt 2\). Infact, \(\sqrt[n]{x}\) is the same as \(x^{\frac {1}{n}}\).

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ask google

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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.

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read NCERT of class 8 chapter 6

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read NCERT of class 8 chapter 6

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around 1.414

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by using taylor - macloren method

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take a calculator.the type like this (2)^1/2.then press "=".you will get the answer.

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Le V is correct....

its 1.414

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Comment deleted May 12, 2013

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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-How

tofindsquarerootofanumberLongdivisionmethodSquaresandsquarerootsCheck these. Hope it helps!

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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...Log in to reply

Use scientific calculator.

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