+0  
 
0
583
3
avatar

how do you calculate the cube root without calculator

Guest May 29, 2014

Best Answer 

 #3
avatar+27229 
+5

The iterative method Bertie mentioned, to find the cube root of "a", say, is:

$$$$x_{n+1}=\frac{1}{3}(\frac{a}{x_n^2}+2x_n)$$

This is derived using Newton-Raphson.

However, in general, I wouldn't want to use this without a calculator of some sort! 

Alan  May 31, 2014
 #2
avatar+890 
+5

There is, I vaguely remember, an algebraic method similar to that for calculating square roots and it's also possible to use the Newton-Raphson method, (though you would need to be good at arithmetic, hardly the sort of calculation you would attempt without a calculator).

If the number is close to some convenient cube, it's possible to make use of the binomial expansion. For example.

$$\begin{array}{lcl}
\sqrt[3]{1005}&=&(1000+5)^{1/3}\\
&=&1000^{1/3}(1+0.005)^{1/3}\\
&=&10(1+(1/3)0.005+(1/3)(-2/3)0.005^{2}/2!+\dots)\\
&=&10(1+0.0016667-0.0000028+\dots)\\
&\approx&10.016639
\end{array}$$

That's easily done on paper and is correct to 6dp.

Bertie  May 30, 2014
 #3
avatar+27229 
+5
Best Answer

The iterative method Bertie mentioned, to find the cube root of "a", say, is:

$$$$x_{n+1}=\frac{1}{3}(\frac{a}{x_n^2}+2x_n)$$

This is derived using Newton-Raphson.

However, in general, I wouldn't want to use this without a calculator of some sort! 

Alan  May 31, 2014
 #4
avatar+92763 
0

That's an interesting tecnique, Alan and Bertie......

I'm with Alan...........a calculator seems vital......

 

CPhill  May 31, 2014

8 Online Users

avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.