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√ How can I get √ without using calculator

 Apr 15, 2014
 #1
avatar+103676 
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Re: √ How can I get without using calculator

Even a calculator will only give you an approximate answer for most square roots.  For, most square roots are irrational numbers and can not be expressed exactly in number form.

Can you give a specific example of a question?

 Apr 15, 2014
 #2
avatar+28129 
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You can estimate the square root of a number n by iterating the expression (1/2)(n+2/n).  That is, you get the first estimate by n1 = (1/2)(n+2/n), then the second, better, estimate by n2 = (1/2)(n1+2/n1), then the third estimate by n3 = (1/2)(n2+2/n2) and so on.  However, you will probably still need a calculator to do these calculations!!

 Apr 15, 2014
 #3
avatar+6 
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you can by dividing by 2 from the number the u are finding the square root  

 Apr 15, 2014
 #4
avatar+890 
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The iteration in the previous post converges to the square root of 2.

For convergence to the square root of N, the formula should be

$$x_{i+1}=\frac{1}{2}\left(x_{i}+\frac{N}{x_{i}}\right)$$.

 Apr 16, 2014

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