Question

find the cube root of 1728 by prime factorization​

Answer 1

prime factorization of

1728 = 2×2×2×2×2×2×3×3×3

cube root of 1728 = 2×2× 3

= 12

Answer 2

First we have to find the factors of 1728, You can find it by dividing method.

2 |1728

2 |864

2 |432

2 |216

2 |108

2 |54

3 |27

3 |9

3 |3

1

Hence 1728 = 2×2×2×2×2×2×3×3×3

so ∛1728 = ∛(2×2×2×2×2×2×3×3×3)

=> ∛1728 = ∛(2³×2³×3³)

=> ∛1728 = 2×2×3

=> ∛1728 = 12

Hope it helps.