Subjective Type

Which of the following are not perfect cubes? (i) 216 (ii) 128 (iii) 1000 (iv) 100 (v) 46656

Solution

(i) $$216 = 2\times 2\times2 \times 3\times 3\times 3 =$$ $$ 2^{3}\times 3^{3} = 6^3$$
So, $$216$$ is a perfect cube.

(ii) $$128 =2\times 2\times 2\times 2\times 2\times 2\times 2$$
$$=$$ $$ 2^{3} \times 2^{3} \times 2 = 6^3\times2$$
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.

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