#### Chapters

Chapter 2: Powers

Chapter 3: Squares and Square Roots

Chapter 4: Cubes and Cube Roots

Chapter 5: Playing with Numbers

Chapter 6: Algebraic Expressions and Identities

Chapter 7: Factorization

Chapter 8: Division of Algebraic Expressions

Chapter 9: Linear Equation in One Variable

Chapter 10: Direct and Inverse Variations

Chapter 11: Time and Work

Chapter 12: Percentage

Chapter 13: Proft, Loss, Discount and Value Added Tax (VAT)

Chapter 14: Compound Interest

Chapter 15: Understanding Shapes-I (Polygons)

Chapter 16: Understanding Shapes-II (Quadrilaterals)

Chapter 17: Understanding Shapes-III (Special Types of Quadrilaterals)

Chapter 18: Practical Geometry (Constructions)

Chapter 19: Visualising Shapes

Chapter 20: Mensuration - I (Area of a Trapezium and a Polygon)

Chapter 21: Mensuration - II (Volumes and Surface Areas of a Cuboid and a Cube)

Chapter 22: Mensuration - III (Surface Area and Volume of a Right Circular Cylinder)

Chapter 23: Data Handling-I (Classification and Tabulation of Data)

Chapter 24: Data Handling-II (Graphical Representation of Data as Histograms)

Chapter 25: Data Handling-III (Pictorial Representation of Data as Pie Charts or Circle Graphs)

Chapter 26: Data Handling-IV (Probability)

Chapter 27: Introduction to Graphs

#### RD Sharma Mathematics Class 8 by R D Sharma (2019-2020 Session)

## Chapter 4: Cubes and Cube Roots

#### RD Sharma solutions for Class 8 Maths Chapter 4 Exercise 4.1 [Pages 7 - 9]

Find the cubes of the number 7 .

Find the cubes of the number 12 .

Find the cubes of the number 16 .

Find the cubes of the number 21 .

Find the cubes of the number 40 .

Find the cubes of the number 55 .

Find the cubes of the number 100 .

Find the cubes of the number 302 .

Find the cubes of the number 301 .

Write the cubes of all natural numbers between 1 and 10 and verify the following statements:

(i) Cubes of all odd natural numbers are odd.

(ii) Cubes of all even natural numbers are even.

Observe the following pattern:

1^{3} = 1

1^{3} + 2^{3} = (1 + 2)^{2}

1^{3} + 2^{3} + 3^{3} = (1 + 2 + 3)^{2}

Write the next three rows and calculate the value of 1^{3} + 2^{3 }+ 3^{3} + ... + 9^{3 }+ 10^{3} by the above pattern.

Write the cubes of 5 natural numbers which are multiples of 3 and verify the followings:

'The cube of a natural number which is a multiple of 3 is a multiple of 27'

Write the cubes of 5 natural numbers which are of the form 3*n* + 1 (e.g. 4, 7, 10, ...) and verify the following:

'The cube of a natural number of the form 3*n* + 1 is a natural number of the same form i.e. when divided by 3 it leaves the remainder 1'.

Write the cubes of 5 natural numbers of the form 3*n* + 2 (i.e. 5, 8, 11, ...) and verify the following:

'The cube of a natural number of the form 3*n* + 2 is a natural number of the same form i.e. when it is dividend by 3 the remainder is 2'.

Write the cubes of 5 natural numbers of which are multiples of 7 and verify the following:

'The cube of a multiple of 7 is a multiple of 7^{3}'.

Which of the following is perfect cube?

64

Which of the following is perfect cube?

216

Which of the following is perfect cube?

243

Which of the following is perfect cube?

1000

Which of the following is perfect cube?

1728

Which of the following is perfect cube?

3087

Which of the following is perfect cube?

4608

Which of the following is perfect cube?

106480

Which of the following is perfect cube?

166375

Which of the following is perfect cube?

456533

Which of the following are cubes of even natural numbers?

216, 512, 729, 1000, 3375, 13824

Which of the following are cubes of odd natural numbers?

125, 343, 1728, 4096, 32768, 6859

What is the smallest number by which the following number must be multiplied, so that the products is perfect cube?

675

What is the smallest number by which the following number must be multiplied, so that the products is perfect cube?

1323

What is the smallest number by which the following number must be multiplied, so that the products is perfect cube?

2560

7803

107811

35721

By which smallest number must the following number be divided so that the quotient is a perfect cube?

675

By which smallest number must the following number be divided so that the quotient is a perfect cube?

8640

By which smallest number must the following number be divided so that the quotient is a perfect cube?

1600

8788

7803

107811

35721

243000

Prove that if a number is trebled then its cube is 27 times the cube of the given number.

What happens to the cube of a number if the number is multiplied by 3?

What happens to the cube of a number if the number is multiplied by 4?

What happens to the cube of a number if the number is multiplied by 5?

Find the volume of a cube, one face of which has an area of 64 m^{2}.

Find the volume of a cube whose surface area is 384 m^{2}.

Evaluate the following:

Evaluate the following:

Write the units digit of the cube of each of the following numbers:

31, 109, 388, 833, 4276, 5922, 77774, 44447, 125125125

Find the cubes of the following number by column method 35.

Find the cubes of the following number by column method 56 .

Find the cubes of the following number by column method 72 .

Which of the following number is not perfect cubes?

64

Which of the following number is not perfect cubes?

216

Which of the following number is not perfect cubes?

243

Which of the following number is not perfect cubes?

1728

For of the non-perfect cubes in Q. No. 20 find the smallest number by which it must be multiplied so that the product is a perfect cube.

For of the non-perfect cubes in Q. No. 20 find the smallest number by which it must be divided so that the quotient is a perfect cube.

By taking three different values of *n* verify the truth of the following statement:

If *n* is even , then *n*^{3} is also even.

By taking three different values of *n* verify the truth of the following statement:

If *n* is odd, then *n*^{3} is also odd.

By taking three different values of *n* verify the truth of the following statement:

If *n* leaves remainder 1 when divided by 3, then *n*^{3} also leaves 1 as remainder when divided by 3.

By taking three different values of *n* verify the truth of the following statement:

If a natural number *n* is of the form 3*p* + 2 then *n*^{3} also a number of the same type.

Write true (T) or false (F) for the following statement:

392 is a perfect cube.

Write true (T) or false (F) for the following statement:

8640 is not a perfect cube.

Write true (T) or false (F) for the following statement:

No cube can end with exactly two zeros.

Write true (T) or false (F) for the following statement:

There is no perfect cube which ends in 4.

Write true (T) or false (F) for the following statement:

For an integer *a*, *a*^{3} is always greater than *a*^{2}.

Write true (T) or false (F) for the following statement:

If *a* and *b* are integers such that *a*^{2} > *b*^{2}, then *a*^{3} > *b*^{3}.

Write true (T) or false (F) for the following statement:

If *a* divides *b*, then *a*^{3} divides *b*^{3}.

Write true (T) or false (F) for the following statement:

If *a*^{2}^{ }ends in 9, then *a*^{3} ends in 7.

Write true (T) or false (F) for the following statement:

If* **a*^{2} ends in 5, then* a*^{3} ends in 25.

Write true (T) or false (F) for the following statement:

If *a*^{2} ends in an even number of zeros, then *a*^{3} ends in an odd number of zeros.

#### RD Sharma solutions for Class 8 Maths Chapter 4 Exercise 4.2 [Page 13]

Find the cube of −11 .

Find the cube of −12 .

Find the cube of −21 .

Which of the following number is cube of negative integer - 64 .

Which of the following number is cube of negative integer - 1056 .

Which of the following number is cube of negative integer - 2197.

Which of the following number is cube of negative integer - 2744 .

Which of the following number is cube of negative integer - 42875 .

Show that the following integer is cube of negative integer. Also, find the integer whose cube is the given integer −5832 .

Show that the following integer is cube of negative integer. Also, find the integer whose cube is the given integer −2744000 .

Find the cube of \[\frac{7}{9}\] .

Find the cube of \[- \frac{8}{11}\] .

Find the cube of \[\frac{12}{7}\] .

Find the cube of \[- \frac{13}{8}\] .

Find the cube of \[2\frac{2}{5}\] .

Find the cube of:

Find the cube of 0.3 .

Find the cube of 1.5 .

Find the cube of 0.08 .

Find the cube of 2.1 .

Find which of the following number is cube of rational number \[\frac{27}{64}\] .

Find which of the following number is cube of rational number \[\frac{125}{128}\] .

Find which of the following number is cube of rational number 0.001331 .

Find which of the following number is cube of rational number 0.04 .

#### RD Sharma solutions for Class 8 Maths Chapter 4 Exercise 4.3 [Pages 21 - 22]

Find the cube rootsof the following number by successive subtraction of number:

1, 7, 19, 37, 61, 91, 127, 169, 217, 271, 331, 397, ... 64 .

Find the cube root of the following number by successive subtraction of number:

1, 7, 19, 37, 61, 91, 127, 169, 217, 271, 331, 397, ... 512 .

Find the cube root of the following number by successive subtraction of number:

1, 7, 19, 37, 61, 91, 127, 169, 217, 271, 331, 397, ... 1728 .

Using the method of successive subtraction examine whether or not the following numbers is perfect cube 130 .

Using the method of successive subtraction examine whether or not the following numbers is perfect cube 345 .

Using the method of successive subtraction examine whether or not the following numbers is perfect cube 792 .

Using the method of successive subtraction examine whether or not the following numbers is perfect cube 1331 .

Find the smallest number that must be subtracted from those of the numbers in question 2 which are not perfect cubes, to make them perfect cubes. What are the corresponding cube roots?

Find the cube root of the following natural number 343 .

Find the cube root of the following natural number 2744 .

Find the cube root of the following natural number 4913 .

Find the cube root of the following natural number 1728 .

Find the cube root of the following natural number 35937 .

Find the cube root of the following natural number 17576 .

Find the cube root of the following natural number 134217728 .

Find the cube root of the following natural number 48228544 .

Find the cube root of the following natural number 74088000 .

Find the cube root of the following natural number 157464 .

Find the cube root of the following natural number 1157625 .

Find the cube root of the following natural number 33698267 .

Find the smallest number which when multiplied with 3600 will make the product a perfect cube. Further, find the cube root of the product.

Multiply 210125 by the smallest number so that the product is a perfect cube. Also, find out the cube root of the product.

What is the smallest number by which 8192 must be divided so that quotient is a perfect cube? Also, find the cube root of the quotient so obtained.

Three numbers are in the ratio 1 : 2 : 3. The sum of their cubes is 98784. Find the numbers.

The volume of a cube is 9261000 m^{3}. Find the side of the cube.

#### RD Sharma solutions for Class 8 Maths Chapter 4 Exercise 4.4 [Pages 30 - 31]

Find the cube root of the following integer −125 .

Find the cube root of the following integer −5832 .

Find the cube root of the following integer −2744000 .

Find the cube root of the following integer −753571.

Find the cube root of the following integer −32768 .

Show that: \[\sqrt[3]{27} \times \sqrt[3]{64} = \sqrt[3]{27 \times 64}\]

Show that: \[\sqrt[3]{64 \times 729} = \sqrt[3]{64} \times \sqrt[3]{729}\]

Show that: \[\sqrt[3]{- 125 \times 216} = \sqrt[3]{- 125} \times \sqrt[3]{216}\]

Show that:\[\sqrt[3]{- 125 - 1000} = \sqrt[3]{- 125} \times \sqrt[3]{- 1000}\]

Find the cube root of the following number 8 × 125 .

Find the cube root of the following number −1728 × 216 .

Find the cube root of the following number −27 × 2744 .

Find the cube root of the following number −729 × −15625 .

Evaluate : \[\sqrt[3]{4^3 \times 6^3}\]

Evaluate: \[\sqrt[3]{8 \times 17 \times 17 \times 17}\]

Evaluate: \[\sqrt[3]{700 \times 2 \times 49 \times 5}\]

Evaluate: \[125\sqrt[3]{\alpha^6} - \sqrt[3]{125 \alpha^6}\]

Find the cube root of the following rational number \[\frac{- 125}{729}\] .

Find the cube root of the following rational number \[\frac{10648}{12167}\] .

Find the cube root of the following rational number \[\frac{- 19683}{24389}\] .

Find the cube root of the following rational number \[\frac{686}{- 3456}\] .

Find the cube root of the following rational number \[\frac{- 39304}{- 42875}\] .

Find the cube root of the following rational number 0.001728 .

Find the cube root of the following rational number 0.003375 .

Find the cube root of the following rational number 0.001 .

Find the cube root of the following rational number 1.331 .

Evaluate of the following

\[\sqrt[3]{27} + \sqrt[3]{0 . 008} + \sqrt[3]{0 . 064}\]

Evaluate of the following

\[\sqrt[3]{1000} + \sqrt[3]{0 . 008} - \sqrt[3]{0 . 125}\]

Evaluate of the following

\[\sqrt[3]{\frac{729}{216}} \times \frac{6}{9}\]

Evaluate of the following

\[\sqrt[3]{\frac{0 . 027}{0 . 008}} \div \sqrt[]{\frac{0 . 09}{0 . 04}} - 1\]

Evaluate of the following

\[\sqrt[3]{0 . 1 \times 0 . 1 \times 0 . 1 \times 13 \times 13 \times 13}\]

Show that:

\[\frac{\sqrt[3]{729}}{\sqrt[3]{1000}} = \sqrt[3]{\frac{729}{1000}}\]

Show that:

\[\frac{\sqrt[3]{- 512}}{\sqrt[3]{343}} = \sqrt[3]{\frac{- 512}{343}}\]

\[\sqrt[3]{125 \times 27} = 3 \times . . .\]

\[\sqrt[3]{8 \times . . .} = 8\]

\[\sqrt[3]{1728} = 4 \times . . .\]

\[\sqrt[3]{480} = \sqrt[3]{3} \times 2 \times \sqrt[3]{. . .}\]

\[\sqrt[3]{} . . . = \sqrt[3]{7} \times \sqrt[3]{8}\]

\[\sqrt[3]{. . .} = \sqrt[3]{4} \times \sqrt[3]{5} \times \sqrt[3]{6}\]

\[\sqrt[3]{\frac{27}{125}} = \frac{. . .}{5}\]

\[\sqrt[3]{\frac{729}{1331}} = \frac{9}{. . .}\]

\[\sqrt[3]{\frac{512}{. . .}} = \frac{8}{13}\]

The volume of a cubical box is 474.552 cubic metres. Find the length of each side of the box.

Three numbers are to one another 2 : 3 : 4. The sum of their cubes is 0.334125. Find the numbers.

Find the side of a cube whose volume is\[\frac{24389}{216} m^3 .\]

Evaluate:

Evaluate:

\[\sqrt[3]{96} \times \sqrt[3]{144}\]

Evaluate:

Evaluate:

\[\sqrt[3]{121} \times \sqrt[3]{297}\]

Find The cube root of the numbers 3048625, 20346417, 210644875, 57066625 using the fact that 3048625 = 3375 × 729 .

Find The cube root of the numbers 3048625, 20346417, 210644875, 57066625 using the fact that 20346417 = 9261 × 2197 .

Find The cube root of the numbers 3048625, 20346417, 210644875, 57066625 using the fact that 210644875 = 42875 × 4913 .

Find The cube root of the numbers 3048625, 20346417, 210644875, 57066625 using the fact that 57066625 = 166375 × 343 .

Find the units digit of the cube root of the following number 226981 .

Find the units digit of the cube root of the following number 13824 .

Find the units digit of the cube root of the following number 571787 .

Find the units digit of the cube root of the following number 175616 .

Find the tens digit of the cube root of each of the numbers in Q. No. 15.

#### RD Sharma solutions for Class 8 Maths Chapter 4 Exercise 4.5 [Page 36]

Making use of the cube root table, find the cube roots 7

Making use of the cube root table, find the cube root 70 .

Making use of the cube root table, find the cube root

700

Making use of the cube root table, find the cube root

7000

Making use of the cube root table, find the cube root

1100 .

Making use of the cube root table, find the cube root

780 .

Making use of the cube root table, find the cube root

7800

Making use of the cube root table, find the cube root

1346.

Making use of the cube root table, find the cube root

250.

Making use of the cube root table, find the cube root

5112 .

Making use of the cube root table, find the cube root

9800 .

Making use of the cube root table, find the cube root

732 .

Making use of the cube root table, find the cube root

7342 .

Making use of the cube root table, find the cube root

133100 .

Making use of the cube root table, find the cube root

37800 .

Making use of the cube root table, find the cube root

0.27

Making use of the cube root table, find the cube root

8.6 .

Making use of the cube root table, find the cube root

0.86 .

Making use of the cube root table, find the cube root

8.65 .

Making use of the cube root table, find the cube root

7532 .

Making use of the cube root table, find the cube root

833 .

Making use of the cube root table, find the cube root

34.2 .

What is the length of the side of a cube whose volume is 275 cm^{3}. Make use of the table for the cube root.

## Chapter 4: Cubes and Cube Roots

#### RD Sharma Mathematics Class 8 by R D Sharma (2019-2020 Session)

## RD Sharma solutions for Class 8 Mathematics chapter 4 - Cubes and Cube Roots

RD Sharma solutions for Class 8 Maths chapter 4 (Cubes and Cube Roots) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Mathematics for Class 8 by R D Sharma (2019-2020 Session) solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 8 Mathematics chapter 4 Cubes and Cube Roots are Introduction for Cubes, Some Interesting Patterns, Smallest Multiple that is a Perfect Cube, Cube Root Through Prime Factorisation Method, Cube Root of a Cube Number, Introduction of Cubes and Cube Root.

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