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)
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Harrison Lian
·
4 years, 3 months ago

@Harrison Lian
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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

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
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Neeraj Kadian
·
4 years, 3 months ago

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

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

## Comments

Sort by:

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 \[ \sqrt{2} \approx 1.414213562 \] – Đức Việt Lê · 4 years, 3 months ago

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– Vamsi Krishna Appili · 4 years, 3 months ago

u are correctLog in to reply

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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– Justin Wong · 4 years, 3 months ago

Yes very goodLog in to reply

– Đức Việt Lê · 4 years, 3 months ago

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

– Shourya Pandey · 4 years, 3 months ago

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

– Đức Việt Lê · 4 years, 3 months ago

Yes I knew it before I post. But are there any other methods to calculate a power of \[ \frac{1}{n} \] with n integer?Log in to reply

– Vamsi Krishna Appili · 4 years, 3 months ago

ask googleLog in to reply

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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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! – 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 agoLog in to reply

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

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