NCERT Solutions for Class 8 Maths Exercise 7.1

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NCERT Solutions for Class 8 Maths Exercise 7.1 Class 8 Maths book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 8 Maths chapter wise NCERT solution for Maths Book all the chapters can be downloaded from our website and myCBSEguide mobile app for free.

NCERT solutions for Class 8 Maths Cubes and Cube Roots Download as PDF

NCERT Solutions for Class 8 Maths Exercise 7.1

NCERT Solutions for Class 8 Maths Cubes and Cube Roots

Class –VIII Mathematics(Ex. 7.1)
NCERT SOLUTION
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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