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# NCERT Solutions for Class 8 Maths Exercise 7.1 ### myCBSEguide App

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NCERT solutions for Class 8 Maths Cubes and Cube Roots ## NCERT Solutions for Class 8 Maths Cubes and Cube Roots

###### 1. Which of the following numbers are not perfect cubes:

(i)216

(ii)128

(iii)1000

(iv)100

(v)46656

Ans. (i)216

Prime factors of 216 = Here all factors are in groups of 3’s (in triplets) Therefore, 216 is a perfect cube number.

(ii) 128

Prime factors of 128

= 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 = 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

= Here all factors appear in 3’s group.

Therefore, 46656 is a perfect cube. NCERT Solutions for Class 8 Maths Exercise 7.1

###### 2. Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube:

(i)243

(ii)256

(iii)72

(iv)675

(v)100

Ans. (i)243

Prime factors of 243 = Here 3 does not appear in 3’s group.

Therefore, 243 must be multiplied by 3 to make it a perfect cube. ###### (ii) 256

Prime factors of 256

= Here one factor 2 is required to make a 3’s group.

Therefore, 256 must be multiplied by 2 to make it a perfect cube. (iii) 72

Prime factors of 72 = Here 3 does not appear in 3’s group.

Therefore, 72 must be multiplied by 3 to make it a perfect cube. (iv) 675

Prime factors of 675 = Here factor 5 does not appear in 3’s group.

Therefore 675 must be multiplied by 3 to make it a perfect cube. (v)  100

Prime factors of 100 = Here factor 2 and 5 both do not appear in 3’s group.

Therefore 100 must be multiplied by = 10 to make it a perfect cube. NCERT Solutions for Class 8 Maths Exercise 7.1

###### 3. Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube:

(i)81

(ii)128

(iii)135

(iv)192

(v)704

Ans. (i)81

Prime factors of 81 = Here one factor 3 is not grouped in triplets.

Therefore 81 must be divided by 3 to make it a perfect cube. (ii) 128

Prime factors of 128 = Here one factor 2 does not appear in a 3’s group.

Therefore, 128 must be divided by 2 to make it a perfect cube.

###### (iii) 135

Prime factors of 135 = Here one factor 5 does not appear in a triplet.

Therefore, 135 must be divided by 5 to make it a perfect cube. (iv) 192

Prime factors of 192 = Here one factor 3 does not appear in a triplet.

Therefore, 192 must be divided by 3 to make it a perfect cube. (v) 704

Prime factors of 704

= Here one factor 11 does not appear in a triplet.

Therefore, 704 must be divided by 11 to make it a perfect cube. NCERT Solutions for Class 8 Maths Exercise 7.1

###### 4. Parikshit makes a cuboid of plasticine of sides 5 cm, 2 cm, 5 cm. How many such cuboids will he need to form a cube?

Ans. Given numbers = Since, Factors of 5 and 2 both are not in group of three.

Therefore, the number must be multiplied by = 20 to make it a perfect cube.

Hence he needs 20 cuboids.

## NCERT Solutions for Class 8 Maths Exercise 7.1

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### 1 thought on “NCERT Solutions for Class 8 Maths Exercise 7.1”

1. very helpful for me in clearing my doubts thanks a lot !