Question

Find the cube root of $8000$.

Answer 1

Apply prime factorization and calculate cube root

The given number is $8000$.

The prime factors of $8000$ can be calculated as,

$\begin{array}{cc}2& 8000\\ 2& 4000\\ 2& 2000\\ 2& 1000\\ 2& 500\\ 2& 250\\ 5& 125\\ 5& 25\\ 5& 5\\ & 1\end{array}$

So, $8000=2\times 2\times 2\times 2\times 2\times 2\times 5\times 5\times 5$

Then, the cube root of $8000$ is,

$$\begin{gathered} \sqrt[3]{8000}=\sqrt[3]{2\times 2\times 2\times 2\times 2\times 2\times 5\times 5\times 5} \\ \Rightarrow \sqrt[3]{8000}=\sqrt[3]{\overline{2\times 2\times 2}\times \overline{2\times 2\times 2}\times \overline{5\times 5\times 5}} \\ \Rightarrow \sqrt[3]{8000}=2\times 2\times 5 \\ \Rightarrow \sqrt[3]{8000}=20 \end{gathered}$$

Hence, the cube root of $8000$ is $20$.