question_answer

Using prime factorisation, find the cube root of 5832.

Answer:

The prime factorisation of 5832 is                    

2	5832
2	2916
2	1458
3	729
3	243
3	81
3	27
3	9
3	3
	1

\[5832\text{ }=2\times 2\times 2\times 3\times 3\times 3\times 3\times 3\times 3\] Therefore,         \[\sqrt[3]{5832}=\sqrt[3]{2\times 2\times 2\times 3\times 3\times 3\times 3\times 3\times 3}\] \[=2\times 3\times 3\] =18