Ncert solutions

Ncert solutions

Grade 8

Cubes and Cube Roots | Exercise 7.1

Question 1

Q1) Which of the following numbers are not perfect cubes:

(i)216

(ii)128

(iii)1000

(iv)100

(v) 46656

Solution:

(i) 216

Prime factors of 216 = 2\times2\times2\times3\times3\times3

Here all factors are in groups of 3’s (in triplets)

Therefore, 216 is a perfect cube number.

(ii) 128

Prime factors of 128 =

2\times2\times2\times2\times2\times2\times2

Here one factor 2 does not appear in a 3’s group.

Therefore, 128 is not a perfect cube.

(iii) 1000

Prime factors of 1000 = 2\times2\times2\times3\times3\times3

Here all factors appear in 3’s group.

Therefore, 1000 is a perfect cube.

(iv) 100

Prime factors of 100 = 2 x 2 x 5 x 5

Here all factors do not appear in 3’s group.

Therefore, 100 is not a perfect cube.

(v) 46656

Prime factors of 46656 = 2\times2\times2\times2\times2\times2\times3\times3\times3\times3\times3\times3

Here all factors appear in 3’s group.

Therefore, 46656 is a perfect cube.

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subject-cta

Question 1

Q1) Which of the following numbers are not perfect cubes:

(i)216

(ii)128

(iii)1000

(iv)100

(v) 46656

Solution:

(i) 216

Prime factors of 216 = 2\times2\times2\times3\times3\times3

Here all factors are in groups of 3’s (in triplets)

Therefore, 216 is a perfect cube number.

(ii) 128

Prime factors of 128 =

2\times2\times2\times2\times2\times2\times2

Here one factor 2 does not appear in a 3’s group.

Therefore, 128 is not a perfect cube.

(iii) 1000

Prime factors of 1000 = 2\times2\times2\times3\times3\times3

Here all factors appear in 3’s group.

Therefore, 1000 is a perfect cube.

(iv) 100

Prime factors of 100 = 2 x 2 x 5 x 5

Here all factors do not appear in 3’s group.

Therefore, 100 is not a perfect cube.

(v) 46656

Prime factors of 46656 = 2\times2\times2\times2\times2\times2\times3\times3\times3\times3\times3\times3

Here all factors appear in 3’s group.

Therefore, 46656 is a perfect cube.

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subject-cta
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