Question
Using prime factorisation, find the cube root of 5832 .
✓
Answer
The prime factorisation of 5832
$\therefore 5832=\underline{2 \times 2 \times 2} \times \underline{3 \times 3 \times 3} \times \underline{3 \times 3 \times 3}$
Therefore, $\sqrt[3]{5832}$
$\begin{array}{l}=\sqrt[3]{\underline{2 \times 2 \times 2}} \times \underline{3 \times 3 \times 3} \times \underline{3 \times 3 \times 3} \\=2 \times 3 \times 3=18\end{array}$
$\therefore 5832=\underline{2 \times 2 \times 2} \times \underline{3 \times 3 \times 3} \times \underline{3 \times 3 \times 3}$
| 2 | 5832 |
| 2 | 2916 |
| 2 | 1458 |
| 3 | 729 |
| 3 | 243 |
| 3 | 81 |
| 3 | 27 |
| 3 | 9 |
| 3 | 3 |
| 1 |
$\begin{array}{l}=\sqrt[3]{\underline{2 \times 2 \times 2}} \times \underline{3 \times 3 \times 3} \times \underline{3 \times 3 \times 3} \\=2 \times 3 \times 3=18\end{array}$
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