Question

Check whether the following are perfect cubes?
(i) $400$ (ii) $216$ (iii) $729$ (iv) $250$ (v) $1000$ (vi) $900$

Answer 1

Factorizing each number

(i) $400=2^4\times 5^2$ - $\text{Not a perfect cube}$

(ii) $216=2^3\times 3^3$ - $\text{A perfect cube}$

(iii) $729=3^6$ - $\text{A perfect cube}$

(iv) $250=5^3\times 2$ - $\text{Not a perfect cube}$

(v) $1000={10}^3$ - $\text{A perfect cube}$

(vi) $900=3^2\times 2^2\times 5^2$ - $\text{Not a perfect cube}$

Therefore, $216,729,1000\text{are perfect cubes}$.