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

\[5832=2\times 2\times 2\times 3\times 3\times 3\times 3\times 3\times 3\]

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

\[=2\times 3\times 3\]

= 18