NCERT Solutions Class 8 Maths Chapter 7 Cubes and Cube Roots Exercise 7.1

 

Introduction:

In this exercise/article we will learn about cube and cube roots. Cube is 3d picture of square and you will find the cube and cubes roots in this exercise and find cube and cube roots through prime factorisation method and find the perfect cube. You will learn cubes then do this exercise .

 

NCERT Solutions Class 8 Maths Chapter 7 Cubes and Cube Roots :

• NCERT Class 8 Maths Chapter 7 Cubes and Cube Roots Exercise 7.1 
• NCERT Class 8 Maths Chapter 7 Cubes and Cube Roots Exercise 7.2 

Class 8 Maths Exercise 7.1 (Page-114)

Q1. Which of the following numbers are not perfect cubes ?

(i) 216

Solution :

Given 216

we need to find the not perfect cube of 216

216 = 2 × 2 × 2 × 3 × 3 ×3

= \(\displaystyle \underline{{2\,\times \,2\,\times \,2}}\,\times \underline{{3\,\times \,3\,\times \,3}}\)

= 2³ × 3³

= 2 × 3

= 6

So, the perfect cube of 216 is 6

(ii) 128

Solution :

Given 128

we need to find the not perfect cube of 128

128 = 2 × 2 × 2 × 2 × 2 × 2 × 2

= \(\displaystyle \underline{{2\,\times \,2\,\times \,2}}\,\times \underline{{2\,\times \,2\,\times \,2}}\,\times \,2\)

= 2³ × 2³ × 2

= 2 × 2 × 2

= 8

So, 128 is not a perfect cube

(iii) 1000

Solution :

Given 1000

we need to find the not perfect cube of 1000

1000 = 2 × 2 × 2 × 5 × 5 × 5 × 5

= \(\displaystyle \underline{{2\,\times \,2\,\times \,2}}\,\times \underline{{5\,\times \,5\,\times \,5}}\,\times \,5\)

= 2³ × 5³ × 5

= 2 × 5

= 10

So, the perfect cube of 1000 is 10

(iv) 100

Solution :

Given 100

we need to find the not perfect cube of 100

100 = 2 × 2 × 5 × 5

= \(\displaystyle \underline{{2\,\times \,2}}\,\times \,\underline{{5\,\times \,5}}\)

= 2² × 5²

= 2 × 5

= 10

So, 100 is not a perfect cube

(v) 46656

Solution :

Given 46656

we need to find the not perfect cube of 46656

46656 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3

= \(\displaystyle \underline{{2\,\times \,2\,\times \,2}}\,\times \underline{{2\,\times \,2\,\times \,2}}\,\times \,\underline{{3\,\times \,3\,\times \,3\,}}\times \,\underline{{3\,\times \,3\,\times \,3}}\)

= 2³ × 2³ × 3³ × 3³

= 2 × 2 × 3 × 3

= 36

So, the perfect cube of 46656 is 36

Q2. Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube.

(i) 243

Solution :

Given 243

243 = 3 × 3 × 3 × 3 × 3

= \(\displaystyle \underline{{3\,\times \,3\,\times \,3}}\,\times \,\underline{{3\,\times \,3}}\)

= 3³ × 3²

∴ It must be multiplied by 3 to obtain a perfect cube

So, answer is 3

(ii) 256

Solution :

Given 256

256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

= \(\displaystyle \underline{{2\,\times \,2\,\times \,2}}\,\times \,\underline{{2\,\times \,2\,\times \,2}}\,\times \,\underline{{2\,\times \,2}}\)

= 2³ × 2³ × 2²

∴ It must be multiplied by 2 to obtain a perfect cube

= So, answer is 2

(iii) 72

Solution :

Given 72

72 = 2 × 2 × 2 × 3 × 3

= \(\displaystyle \underline{{2\,\times \,2\,\times \,2}}\,\times \,\underline{{3\,\times \,3}}\)

= 2³ × 3²

∴ It must be multiplied by 3 to obtain the perfect cube

So, answer is 3

(iv) 675

Solution :

Given 675

675 = 3 × 3 × 3 × 5 × 5

= \(\displaystyle \underline{{3\,\times \,3\,\times \,3}}\,\times \,\underline{{5\,\times \,5}}\)

= 3³ × 5²

∴ It must be multiplied by 5 to obtain a perfect cube

= So, answer is 5

(v) 100

Solution :

Given 100

100 = 2 × 2 × 5 × 5

= \(\displaystyle \underline{{2\times \,2}}\,\times \,\underline{{5\,\times \,5}}\)

= 2² × 5²

= 2 × 5 = 10               [ each multiplied ]

∴ It must be multiplied by 10 to obtain a perfect cube

So, answer is 10

Q3. Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube.

(i) 81

Solution :

Given 81

81 = 3 × 3 × 3 × 3

= \(\displaystyle \underline{{3\times \,3\,\times \,3}}\,\times \,3\,\)

= 3³ × 3

∴ 81 must be divided by 3 to obtain a perfect cube

So, answer is 3

(ii) 128

Solution :

Given 128

128 = 2 × 2 × 2 × 2 × 2 × 2 × 2

= \(\displaystyle \underline{{2\times \,2\,\times \,2}}\,\times \,\underline{{2\,\times \,2\,\times \,2}}\,\times \,2\,\)

= 2³ × 2³ × 2

∴ 128 must be divided by 2 to obtain a perfect cube

So, answer is 2

(iii) 135

Solution :

Given 135

135 = 3 × 3 × 3 × 5

= \(\displaystyle \underline{{3\times \,3\,\times \,3}}\,\times \,5\,\)

= 3³ × 5

∴ 135 must be divided by 5 to obtain a perfect cube

So, answer is  5

(iv) 192

Solution :

Given 192

192 = 2 × 2 × 2 × 2 × 2 × 2 × 3

= \(\displaystyle \underline{{2\times \,2\,\times \,2}}\,\times \,\underline{{2\times \,2\,\times \,2}}\,\times \,3\)

= 2³ × 2³ × 3

∴ 192 must be divided by 3 to obtain a perfect cube

So, answer is 3

(v) 704

Solution :

Given 704

704 = 2 × 2 × 2 × 2 × 2 × 2 × 11

= \(\displaystyle \underline{{2\times \,2\,\times \,2}}\,\times \,\underline{{2\times \,2\,\times \,2}}\,\times \,11\)

= 2³ × 2³ × 11

∴ 704 must be divided by 11 to obtain a perfect cube

Q4. Parikshit makes a cuboid of plasticine of sides 5cm, 2cm , 5cm. How many such cuboid will he need to form a cube ?

Solution :

Given , side of cuboid is 5cm, 2cm and 5cm

[ Volume of the cuboid = Length × breadth × height ]

= 5 × 2 × 5

= 50

50 = 2 × 5 × 5

= 2 × 5²

= 2 × 2 × 5         [ we need 2² and 5 for complete perfect cube of 2 and 5 ]

= 20 cuboids

So, answer is 20 cuboids .

 

NCERT Solutions Class 8 Maths Chapter 7 Cubes and Cube Roots :

• NCERT Class 8 Maths Chapter 7 Cubes and Cube Roots Exercise 7.1 
• NCERT Class 8 Maths Chapter 7 Cubes and Cube Roots Exercise 7.2