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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....

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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This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

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

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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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ask google

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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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$\frac{1}{n}$ with n integer?

Yes I knew it before I post. But are there any other methods to calculate a power ofLog in to reply

Yes very good

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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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Le V is correct....

its 1.414

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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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by using taylor - macloren method

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around 1.414

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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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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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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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