Question

"Question 1 Which of the following numbers are notperfect cubes? (i) 216 (ii) 128 (iii) 1000 (iv) 100 (v) 46656

Class 8 Cubes and Cube Roots Page 114"

Answer 1

In the prime factorization of a perfect cube every prime factor occurs 3 times.

To determine whether a number is a perfect cube or not proceed as follows:
1.Find the prime factors of the given number.

2. Make Group of 3 equal prime factors.

3. If a group contains only one or two equal prime factors then a given number is not a perfect cube otherwise it is a perfect cube.

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solution:

i)
216 =(2 x 2 x 2 )x ( 3 x 3 x 3)

Hence, 216 has 2 groups of three equal prime factors . Hence, 216 is a perfect cube.


(ii) 128
128 = (2 x 2 x 2 )x (2 x 2 x 2) x 2
Here, 128 has only 2 pairs of equal prime factors .Hence, 128 is not a perfect Cube.


(iii) 1000
1000 = (2 x 2 x 2) × (5×5×5)
Hence, 1000 has 2 groups of three equal prime factors . Hence, 1000 is a perfect cube.

(iv) 100
100 = (2 x 2 )x (5 x 5)

Thus, the group (2 x 2 )x (5 x 5) has Only two prime factors. Hence, 100 is not a perfect Cube.
.
(v) 46656
46656 = (2 x 2 x 2) x (2 x 2 x 2) x (3 x 3 x 3) x (3 x 3 x 3)

Hence, 46656 has 4 groups of three equal prime factors . Hence, 46656 is a perfect cube.

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Hope this will help you......

Answer 2

Answer:

216 is perfect cube please mark me as brainliest answer please