Question
Using prime factorisation, find the cube roots of:
$512$
$512$
✓
Answer
We have, $512$
$\begin{array}{c|c}2 & 512 \\ \hline2 & 256\\\hline2&128\\\hline2&64\\\hline2&32\\\hline2&16\\\hline2&8\\\hline2&4\\\hline2&2\\\hline&1\end{array}$
Now, $512 =2\times2\times2\times2\times2\times2\times2\times2\times2$
$\therefore\sqrt[3]{512}=2\times2\times2$
$=8$
$\begin{array}{c|c}2 & 512 \\ \hline2 & 256\\\hline2&128\\\hline2&64\\\hline2&32\\\hline2&16\\\hline2&8\\\hline2&4\\\hline2&2\\\hline&1\end{array}$
Now, $512 =2\times2\times2\times2\times2\times2\times2\times2\times2$
$\therefore\sqrt[3]{512}=2\times2\times2$
$=8$
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