Find the Cube Root of 1000000

Question

Rigoberto Gordon · Accepted Answer

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}

\Rightarrow 1000000 = 2^{6} * 5^{6}

\Rightarrow 1000000 = (2 * 5)^{6}

\Rightarrow 1000000 = 10^{6}

\Rightarrow \sqrt[3]{1000000} = 10^{3} = 1000

Hence, the cube root of 1000000 is 1000.

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