Question

Which of the following numbers are not perfect cubes?
(i) $128$ (ii) $100$ (iii) $64$ (iv) $125$ (v) $72$ (vi) $625$

Answer 1

Factorizing each number

(i) $128=2^7$ $-$ $\text{Not a perfect cube}$

(ii) $100=2^2\times 5^2$ $-$ $\text{Not a perfect cube}$

(iii) $64=2^6$ $-$ $\text{A perfect cube}$

(iv) $125=5^3$ $-$ $\text{A perfect cube}$

(v) $72=2^3\times 3^2$ $-$ $\text{Not a perfect cube}$

(vi) $625=5^4$ $-$ $\text{Not a perfect cube}$

Therefore, $128,100,72,625$ are not perfect cubes