eVidyarthi

Main Menu
  • eVidyarthi
  • School
    • Class 6th
      • Maths Class 6
      • Science Class 6
      • Hindi Class 6
      • व्याकरण
      • English Class 6
      • English Grammar
      • Sanskrit Class 6
      • Geography
      • Civics
      • History
    • Class 7th
      • Maths Class 7
      • Science Class 7
      • Hindi Class 7
      • व्याकरण
      • English Class 7
      • English Grammar
      • Sanskrit Class 7
      • Geography
      • Civics
      • History
    • Class 8th
      • Maths Class 8
      • Science Class 8
      • Hindi Class 8
      • व्याकरण
      • English Class 8
      • English Grammar
      • Sanskrit Class 8
      • Geography
      • Civics
      • History
    • Class 9th
      • Maths Class 9
      • Science Class 9
      • Hindi Class 9
      • English Class 9
      • English Grammar
      • व्याकरण
      • Economics Class 9
      • Geography Class 9
      • Civics Class 9
      • History Class 9
    • Class 10th
      • Maths Class 10
      • Science Class 10
      • Hindi Class 10
      • English Class 10
      • English Grammar
      • व्याकरण
      • Economics Class 10
      • History Class 10
      • Civics Class 10
      • Geography Class 10
    • Class 11th
      • Maths Class 11
      • Accounts Class 11
      • English Class 11
      • English Grammar
      • व्याकरण
      • Chemistry Class 11
      • Physics Class 11
      • Biology Class 11
    • Class 12th
      • Maths Class 12
      • Accounts Class 12
      • Chemistry Class 12
      • Physics Class 12
      • Biology Class 12
      • English Class 12
      • English Grammar
      • व्याकरण
    • Close
  • English
    • Basic English Grammar
    • Basic English Speaking
    • English Vocabulary
    • English Idioms & Phrases
    • Personality Enhancement
    • Interview Skills
    • Close
  • Softwares
    • Microsoft Word
    • PhotoShop
    • Excel
    • Illustrator
    • PowerPoint
    • Close
Class 8th Maths || Menu
  • Important
    • Sample Paper – I
    • Sample Paper – II
    • Important Formulas
    • Revision Notes
    • MCQs
    • Mathematics Book
    • Close
  • Rational Numbers
    • Ex 1.1
    • Ex 1.2
    • MCQs
    • Ex 1.1 NCERT Solutions
    • Ex 1.2 NCERT Solutions
    • Close
  • Linear Equations in One Variable
    • Ex 2.1
    • Ex 2.2
    • Ex 2.3
    • Ex 2.4
    • Ex 2.5
    • Ex 2.6
    • MCQs
    • Ex 2.1 NCERT Solutions
    • Ex 2.2 NCERT Solutions
    • Ex 2.3 NCERT Solutions
    • Ex 2.4 NCERT Solutions
    • Ex 2.5 NCERT Solutions
    • Ex 2.6 NCERT Solutions
    • Close
  • Understanding Quadrilaterals
    • Ex 3.1
    • Ex 3.2
    • Ex 3.3
    • Ex 3.4
    • MCQs
    • Ex 3.1 NCERT Solutions
    • Ex 3.2 NCERT Solutions
    • Ex 3.3 NCERT Solutions
    • Ex 3.4 NCERT Solutions
    • Close
  • Practical Geometry
    • Ex 4.1
    • Ex 4.2
    • Ex 4.3
    • Ex 4.4
    • Ex 4.5
    • MCQs
    • Ex 4.1 NCERT Solutions
    • Ex 4.2 NCERT Solutions
    • Ex 4.3 NCERT Solutions
    • Ex 4.4 NCERT Solutions
    • Ex 4.5 NCERT Solutions
    • Close
  • Data Handling
    • Ex 5.1
    • Ex 5.2
    • Ex 5.3
    • MCQs
    • Ex 5.1 NCERT Solutions
    • Ex 5.2 NCERT Solutions
    • Ex 5.3 NCERT Solutions
    • Close
  • Squares & Square Root
    • Ex 6.1
    • Ex 6.2
    • Ex 6.3
    • Ex 6.4
    • MCQs
    • Ex 6.1 NCERT Solutions
    • EX 6.2 NCERT Solutions
    • Ex 6.3 NCERT Solutions
    • Ex 6.4 NCERT Solutions
    • Close
  • Cubes and Cube Roots
    • Ex 7.1
    • Ex 7.2
    • MCQs
    • Ex 7.1 NCERT Solutions
    • Ex 7.2 NCERT Solutions
    • Close
  • Comparing Quantities
    • Ex 8.1
    • Ex 8.2
    • Ex 8.3
    • MCQs
    • Ex 8.1 NCERT Solutions
    • Ex 8.2 NCERT Solutions
    • Ex 8.3 NCERT Solutions
    • Close
  • Algebraic Expressions and Identities
    • Ex 9.1
    • Ex 9.2
    • Ex 9.3
    • Ex 9.5
    • MCQs
    • Ex 9.1 NCERT Solutions
    • Ex 9.2 NCERT Solutions
    • Ex 9.3 NCERT Solutions
    • Ex 9.4 NCERT Solutins
    • Ex 9.5 NCERT Solutions
    • Close
  • Visualising Solid Shapes
    • Ex 10.1
    • Ex 10.3
    • MCQs
    • Ex 10.1 NCERT Solutions
    • Ex 10.2 NCERT Solutions
    • Ex 10.3 NCERT Solutions
    • Close
  • Mensuration
    • Ex 11.1
    • Ex 11.2
    • Ex 11.3
    • Ex 11.4
    • MCQs
    • Ex 11.1 NCERT Solutions
    • Ex 11.2 NCERT Solutions
    • Ex 11.3 NCERT Solutions
    • Ex 11.4 NCERT Solutions
    • Close
  • Exponents and Powers
    • Ex 12.1
    • Ex 12.2
    • MCQs
    • Ex 12.1 NCERT Solutions
    • Ex 12.2 NCERT Solutions
    • Close
  • Direct and Inverse Proportions
    • Ex 13.1
    • Ex 13.2
    • MCQs
    • Ex 13.1 NCERT Solutions
    • Ex 13.2 NCERT Solutions
    • Close
  • Factorisation
    • Ex 14.1
    • Ex 14.2
    • Ex 14.3
    • Ex 14.4
    • MCQs
    • Ex 14.1 NCERT Solutions
    • Ex 14.2 NCERT Solutions
    • Ex 14.3 NCERT Solutions
    • Close
  • Introduction to Graphs
    • Ex 15.1
    • Ex 15.2
    • Ex 15.3
    • MCQs
    • Ex 15.1 NCERT Solutions
    • Ex 15.2 NCERT Solutions
    • Ex 15.3 NCERT Solutions
    • Close
  • Playing with Numbers
    • Ex 16.1
    • Ex 16.2
    • MCQs
    • Ex 16.1 NCERT Solutions
    • Ex 16.2 NCERT Solutions
    • Close

Class 8 Ex. 7.1 Maths NCERT Solutions

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

Ex 7.1 Class 8 Maths Question 1.
Which of the following numbers are not perfect cubes?

(i) 216

(ii) 128

(iii) 1000

(iv) 100

(v) 46656

Solution:

(i) Prime factorisation of 216 is:

216 = 2 × 2 × 2 × 3 × 3 × 3

In the above factorisation, 2 and 3 have formed a group of three.
Thus, 216 is a perfect cube.

(ii) Prime factorisation of 128 is:

128 = 2 × 2 × 2 × 2 × 2 × 2 × 2

Here, 2 is left without making a group of three.
Thus 128 is not a perfect cube.

(iii) Prime factorisation of 1000, is:

1000 = 2 × 2 × 2 × 5 × 5 × 5

Here, no number is left for making a group of three.
Thus, 1000 is a perfect cube.

(iv) Prime factorisation of 100, is:

100 = 2 × 2 × 5 × 5

Here 2 and 5 have not formed a group of three.
Thus, 100 is not a perfect cube.

(v) Prime factorisation of 46656 is:

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

Here 2 and 3 have formed the groups of three.
Thus, 46656 is a perfect cube.

Ex 7.1 Class 8 Maths Question 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

Solution:

(i) Prime factorisation of 243, is:

243 = 3 × 3 × 3 × 3 × 3 = 3³ × 3 × 3

Here, number 3 is required to make 3 × 3 a group of three, i.e., 3 × 3 × 3
Thus, the required smallest number to be multiplied is 3.

(ii) Prime factorisation of 256, is:

256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2³ × 2³ × 2 × 2

Here, a number 2 is needed to make 2 × 2 a group of three, i.e., 2 × 2 × 2
Thus, the required smallest number to be multiplied is 2.

(iii) Prime factorisation of 72, is:

72 = 2 × 2 × 2 × 3 × 3 = 2³ × 3 × 3

Here, a number 3 is required to make 3 × 3 a group of three, i.e. 3 × 3 × 3
Thus, the required smallest number to be multiplied is 3.

(iv) Prime factorisation of 675, is:

675 = 3 × 3 × 3 × 5 × 5 = 3³ × 5 × 5

Here, a number 5 is required to make 5 × 5 a group of three to make it a perfect cube, i.e. 5 × 5 × 5
Thus, the required smallest number is 5.

(v) Prime factorisation of 100, is:

100 = 2 × 2 × 5 × 5

Here, number 2 and 5 are needed to multiplied 2 × 2 × 5 × 5 to make it a perfect cube, i.e., 2 × 2 × 2 × 5 × 5 × 5
Thus, the required smallest number to be multiplied is 2 × 5 = 10.

Ex 7.1 Class 8 Maths Question 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) 92

(v) 704

Solution:

(i) Prime factorisation of 81, is:

81 = 3 × 3 × 3 × 3 = 3³ × 3

Here, a number 3 is the number by which 81 is divided to make it a perfect cube,
i.e., 81 ÷ 3 = 27 which is a perfect cube.
Thus, the required smallest number to be divided is 3.

(ii) Prime factorisation of 128, is:

128 = 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2³ × 2³ × 2

Here, a number 2 is the smallest number by which 128 is divided to make it a perfect cube,
i.e., 128 ÷ 2 = 64 which is a perfect cube.
Thus, 2 is the required smallest number.

(iii) Prime factorisation of 135 is:

135 = 3 × 3 × 3 × 5 = 3³ × 5

Here, 5 is the smallest number by which 135 is divided to make a perfect cube,
i.e., 135 ÷ 5 = 27 which is a perfect cube.
Thus, 5 is the required smallest number.

(iv) Prime factorisation of 192 is:

192 = 2 × 2 × 2 × 2 × 2 × 2 × 3 = 2³ × 2³ × 3

Here, 3 is the smallest number by which 192 is divided to make it a perfect cube,
i.e., 192 ÷ 3 = 64 which is a perfect cube.
Thus, 3 is the required smallest number.

(v) Prime factorisation of 704 is:

704 = 2 × 2 × 2 × 2 × 2 × 2 × 11 = 2³ × 2³ × 11

Here, 11 is the smallest number by which 704 is divided to make it a perfect cube,
i.e., 704 ÷ 11 = 64 which is a perfect cube.
Thus, 11 is the required smallest number.

Ex 7.1 Class 8 Maths Question 4.
Parikshit makes a cuboid of plasticine of sides 5 cm, 2 cm, 5 cm. How many such cuboids will be needed to form a cube?

Solution:

The sides of the cuboid are given as 5 cm, 2 cm and 5 cm.
Volume of the cuboid = 5 cm × 2 cm × 5 cm = 50 cm³
For the prime factorisation of 50, we have
50 = 2 × 5 × 5
To make it a perfect cube, we must have
2 × 2 × 2 × 5 × 5 × 5
= 20 × (2 × 5 × 5)
= 20 × volume of the given cuboid
Thus, the required number of cuboids = 20.

 

Android App

eVidyarthi

Search On eVidyarthi

Evidyarthi on Facebook

Like us on Facebook

Follow Evidyarthi on Youtube

Learn English
Learn English Through हिन्दी
Job Interview Skills
English Grammar
हिंदी व्याकरण - Vyakaran
Mathematics Class 6th
Science Class 6th
हिन्दी Class 6th
Mathematics Class 7th
Science Class 7th
हिन्दी Class 7th
Mathematics Class 8th
Science Class 8th
हिन्दी Class 8th
Mathematics Class 9th
English Class 9th
Science Class 9th
Mathematics Class 10th
English Class 10th
Mathematics Class XI
Chemistry Class XI
Accountancy Class 11th
Accountancy Class 12th
Mathematics Class 12th
Microsoft Word
Microsoft Excel
Microsoft PowerPoint
Adobe PhotoShop
Adobe Illustrator
Learn German
Learn French
IIT JEE
Privacy Policies, Contact Us
Copyright © 2020 eVidyarthi and its licensors. All Rights Reserved.