Question

Find the Cube Root of $1000000$

Answer 1

Find the cube root of given number using prime factorisation

Given, $1000000$

$$\begin{gathered} \begin{array}{cc}2& 1000000\\ 2& 500000\\ 2& 250000\\ 2& 125000\\ 2& 62500\\ 2& 31250\\ 5& 15625\\ 5& 3125\\ 5& 625\\ 5& 125\\ 5& 25\\ 5& 5\\ & 1\end{array} \\ \Rightarrow 1000000=2^6·5^6 \\ \Rightarrow 1000000={(2·5)}^6 \\ \Rightarrow 1000000={10}^6 \\ \Rightarrow \sqrt[3]{1000000}={10}^3=1000 \end{gathered}$$

Therefore, the cube root of $1000000$ is $1000$.