. Which of the following are not perfect cubes

(i) 216 (ii) 128 (iii) 1000 (iv) 100 (v) 46656

Best Answer


(i) 216

Prime factorisation is 2x2x2x3x3x3

Here, two pairs are formed 23x33.

So, 216 is a perfect cube.

(ii) 128

Prime factorisation is 2x2x2x2x2x2x2

Two pairs of 23x23 is formed and one factor 2 is remaining.

 It is not a perfect cube.

(iii) 1000

Prime factorisation is 10x10x10

one pair of 103 is formed.

 It is a perfect cube.

(iv) 100

Prime factorisation is 10x10

There are no pair of three.

It is not a perfect cube.

(v) 46656

Prime factorisation of is 2x2x2x2x2x2x3x3x3x3x3x3

4 pairs of 23x23x33x33 are formed.

It is a perfect cube.

Final Answer:

Hence, 128 and 100 are not perfect cubes.

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