root value

How to caluclate root of 2

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

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 - 8 years, 1 month ago

u are correct

Vamsi Krishna Appili - 8 years, 1 month ago

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

Harrison Lian - 8 years, 1 month ago

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

Đức Việt Lê - 8 years, 1 month ago

ask google

Vamsi Krishna Appili - 8 years, 1 month 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 $x^{\frac {1}{n}}$ .

Shourya Pandey - 8 years, 1 month ago

@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 - 8 years, 1 month ago

Yes very good

Justin Wong - 8 years, 1 month 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....

Sayan Chaudhuri - 8 years, 1 month ago

Le V is correct....

its 1.414

Vamsi Krishna Appili - 8 years, 1 month ago

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

Sreehari Vp - 8 years, 1 month ago

by using taylor - macloren method

Ahmed Magdy - 8 years, 1 month ago

around 1.414

Tan Li Xuan - 8 years, 1 month ago

read NCERT of class 8 chapter 6

Genious Boy - 8 years ago

read NCERT of class 8 chapter 6

Neeraj Kadian - 8 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.

Jason Martin - 8 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...

Shubham Sharma - 8 years, 1 month ago

Use scientific calculator.

Gil Deon Basa - 8 years, 1 month ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$