Question

What is the smallest number that must be multiplied by 1,42,884 to make it a perfect cube?​

Answer 1

Answer:

A number is a prefect cube only when each factor in the prime factorization is grouped in triples.

Steps: 

(i)



216=2×2×2×3×3×3=23×33=(2×3)3=63216=2×2×2×3×3×3=23×33=(2×3)3=63

∴216∴216 is a perfect cube

 (ii)



128=2×2×2×2×2×2×2128=2×2×2×2×2×2×2

128=23×23×2128=23×23×2 one of the 22 is not grouped in triples

∴128∴128 is not a perfect cube

 (iii)   



1000=2×2×2×5×5×51000=23×531000=2×2×2×5×5×51000=23×53

∴1000∴1000 is a perfect cube

(iv) 



100=2×2×5×5=22×5