Cube root: Difference between revisions

From Elliptic Curve Crypto
m x = no. so far written
next step
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{}+30\times 21 \times\_^2+\_^3&=&
{}+30\times 21 \times\_^2+\_^3&=&
\end{array}</math>
\end{array}</math>
 
<blockquote><math display="block">\begin{array}{rrr|rrrr}
To be continued <ref>WikiHow: How to Calculate Cube Root by Hand https://www.wikihow.com/Calculate-Cube-Root-by-Hand</ref> ...
&&&2&1&8\\ \hline
&&\sqrt[3]{}&10&460&353&203\\
\underline2^3&=&8&-8&\downarrow\\ \hline
300\times 2^2\times\underline1&&&2&460\\
{}+30\times 2\times\underline1^2+\underline1^3&=&1261&-1&261&\downarrow\\ \hline
300\times 21^2 \times 8&&&1&199&353\\
{}+30\times 21 \times8^2+8^3&=&1099232&-1&099&232\\ \hline
&&&&100&121
\end{array}</math></blockquote>To be continued <ref>WikiHow: How to Calculate Cube Root by Hand https://www.wikihow.com/Calculate-Cube-Root-by-Hand</ref> ...

Revision as of 01:38, 27 December 2024


Extracting cube roots by hand

Start by grouping the digits under the radical into groups of three as you normally would. This seems natural to do, even if it is a little more

The first step here is to find the largest digit whose cube does not exceed the first group of digits under the radical, cube it, subtract to find the remainder, and bring down the next three digits.

The next step is based on the identity

if we let , the number written so far above the radical, and y be the next digit to calculate. The term has already been subtracted when we bring down the next group of three digits, so the next digit to write above the radical will be the largest y such that .

To be continued [1] ...

  1. WikiHow: How to Calculate Cube Root by Hand https://www.wikihow.com/Calculate-Cube-Root-by-Hand