Question

find the cube root of the following cubic number by prime factorisation for -5832

Answer 1

Solution by prime factorization:

5832−−−−√358323

=23⋅36−−−−−√3=23⋅363

=21⋅32=21⋅32

=2⋅9


=18

Answer 2

2 |5832
2 |2916
2 |1458
3 |729
3 |243
3 |81
3 |27
3 |9
3 |3
|1 So 5832=2×2×2×3×3×3×3×3×3=
${2}^{3} \times {3}^{6} = {18}^{3}$

${( - 1)}^{3} = - 1$
So the cube root of -5832 by prime factorisation is -18. Hope it helps you...