Cubes and Cube Roots Exercise 7.1
NCERT solutions for Class 8 Maths Cubes and Cube Roots
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.