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2023-02-21

Find the Cube Root of $1000000$

Rigoberto Gordon

Determine the cube root of the specified number through prime factorization.
We have, $1000000$
$\begin{array}{cc}2& 1000000\\ 2& 500000\\ 2& 250000\\ 2& 125000\\ 2& 62500\\ 2& 31250\\ 5& 15625\\ 5& 3125\\ 5& 625\\ 5& 125\\ 5& 25\\ 5& 5\\ & 1\end{array}$
$⇒1000000={2}^{6}\ast {5}^{6}$
$⇒1000000=\left(2\ast 5{\right)}^{6}$
$⇒1000000={10}^{6}$
$⇒\sqrt[3]{1000000}={10}^{3}=1000$
Hence, the cube root of 1000000 is 1000.

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