Question

which of the following number is not perfect cube? 216,128,343,1000​

Answer 1

Step-by-step explanation:

(I) $216 \\ = 2 \times 2 \times 2 \times 3 \times \times 3 \times 3 \\ = {2}^{3} \times {3}^{3} \\ = {6}^{3}$

So, 216 is a perfect cube.

(II)$128 \\ = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \\ = {2}^{2} \times {2}^{2} \times 2 \\ = {6}^{3} \times 2$

So, 128 is not a perfect cube.

(III)$1000 \\ = 2 \times 2 \times 2 \times 5 \times 5 \times 5 \\ = {10}^{3}$

So, 1000 is a perfect cube.

(IV)$100 \\ = 2 \times 2 \times 5 \times 5 \\ = {10}^{2}$

So, 100 is not a perfect cube

(V)$46656 \\ = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \\ = {36}^{3}$

So, 46656 is a perfect cube.