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Which of the following are not perfect cubes?

(a) 216

(b) 128

(c) 1000

(d) 100

(e) 46656

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a and b

b, c and d

a, c and e

all

answer is C.

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Detailed Solution

Numbers given are,
(a) 216
(b) 128
(c) 1000
(d) 100
(e) 46656
Factor form of first number,

216 = 2 \times 2 \times 2 \times 3 \times 3 \times 3

216 = 2^{3} \times 3^{3}

216 = 6^{3}

This number is perfect cube.
Factor form of second number,

128 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2

128 = 2^{3} \times 2^{3} \times 2

128 = 6^{3} \times 2

This number is not a perfect cube.
Factor form of third number,

1000 = 2 \times 2 \times 2 \times 5 \times 5 \times 5

1000 = 2^{3} \times 5^{3}

1000 = 10^{3}

This number is perfect cube.
Factor form of forth number,

100 = 2 \times 2 \times 5 \times 5

100 = 10^{2}

This number is perfect square not perfect cube.
Factor form of fifth number,

46656 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3

46656 = 36^{3}

This number is perfect cube.
Here, a, c and e are the perfect cube.
Correct option is 3.

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