# root value

How to caluclate root of 2

Note by Sai Venkata Raju Nanduri
5 years 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 $\sqrt{2} \approx 1.414213562$

- 5 years ago

u are correct

- 5 years ago

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....

- 5 years ago

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

- 5 years ago

Yes very good

- 5 years ago

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

- 5 years 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 $$x^{\frac {1}{n}}$$.

- 5 years 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?

- 5 years ago

- 5 years 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.

- 5 years ago

read NCERT of class 8 chapter 6

- 5 years ago

read NCERT of class 8 chapter 6

- 5 years ago

around 1.414

- 5 years ago

by using taylor - macloren method

- 5 years ago

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

- 5 years ago

Le V is correct....

its 1.414

- 5 years ago

Comment deleted May 12, 2013

You can use long division method:

http://nrich.maths.org/5955

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

Check these. Hope it helps!

- 5 years ago

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...

- 5 years ago

Use scientific calculator.

- 5 years ago