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Chapters
2: Powers
3: Squares and Square Roots
▶ 4: Cubes and Cube Roots
5: Playing with Numbers
6: Algebraic Expressions and Identities
7: Factorization
8: Division of Algebraic Expressions
9: Linear Equation in One Variable
10: Direct and Inverse Variations
11: Time and Work
12: Percentage
13: Proft, Loss, Discount and Value Added Tax (VAT)
14: Compound Interest
15: Understanding Shapes-I (Polygons)
16: Understanding Shapes-II (Quadrilaterals)
17: Understanding Shapes-III (Special Types of Quadrilaterals)
18: Practical Geometry (Constructions)
19: Visualising Shapes
20: Mensuration - I (Area of a Trapezium and a Polygon)
21: Mensuration - II (Volumes and Surface Areas of a Cuboid and a Cube)
22: Mensuration - III (Surface Area and Volume of a Right Circular Cylinder)
23: Data Handling-I (Classification and Tabulation of Data)
24: Data Handling-II (Graphical Representation of Data as Histograms)
25: Data Handling-III (Pictorial Representation of Data as Pie Charts or Circle Graphs)
26: Data Handling-IV (Probability)
27: Introduction to Graphs
![R.D. Sharma solutions for Mathematics [English] Class 8 chapter 4 - Cubes and Cube Roots - Shaalaa.com](/images/mathematics-english-class-8_6:d71f9951bde04f9981d965449678818b.jpg "R.D. Sharma solutions for Mathematics [English] Class 8 chapter 4 - Cubes and Cube Roots")
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Solutions for Chapter 4: Cubes and Cube Roots
Below listed, you can find solutions for Chapter 4 of CBSE R.D. Sharma for Mathematics [English] Class 8.
R.D. Sharma solutions for Mathematics [English] Class 8 4 Cubes and Cube Roots 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.
Find if the following number is not a perfect cube?
243
Observe the following pattern:
13 = 1
13 + 23 = (1 + 2)2
13 + 23 + 33 = (1 + 2 + 3)2
Write the next three rows and calculate the value of 13 + 23 + 33 + ... + 93 + 103 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 3n + 1 (e.g. 4, 7, 10, ...) and verify the following:
'The cube of a natural number of the form 3n + 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 3n + 2 (i.e. 5, 8, 11, ...) and verify the following:
'The cube of a natural number of the form 3n + 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 73'.
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
What is the smallest number by which the following number must be multiplied, so that the products is perfect cube?
7803
What is the smallest number by which the following number must be multiplied, so that the products is perfect cube?
107811
What is the smallest number by which the following number must be multiplied, so that the products is perfect cube?
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
By which smallest number must the following number be divided so that the quotient is a perfect cube?
8788
By which smallest number must the following number be divided so that the quotient is a perfect cube?
7803
By which smallest number must the following number be divided so that the quotient is a perfect cube?
107811
By which smallest number must the following number be divided so that the quotient is a perfect cube?
35721
By which smallest number must the following number be divided so that the quotient is a perfect cube?
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 m2.
Find the volume of a cube whose surface area is 384 m2.
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?
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 n3 is also even.
By taking three different values of n verify the truth of the following statement:
If n is odd, then n3 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 n3 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 3p + 2 then n3 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, a3 is always greater than a2.
Write true (T) or false (F) for the following statement:
If a and b are integers such that a2 > b2, then a3 > b3.
Write true (T) or false (F) for the following statement:
If a divides b, then a3 divides b3.
Write true (T) or false (F) for the following statement:
If a2 ends in 9, then a3 ends in 7.
Write true (T) or false (F) for the following statement:
If a2 ends in 5, then a3 ends in 25.
Write true (T) or false (F) for the following statement:
If a2 ends in an even number of zeros, then a3 ends in an odd number of zeros.
R.D. Sharma solutions for Mathematics [English] Class 8 4 Cubes and Cube Roots 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 .
R.D. Sharma solutions for Mathematics [English] Class 8 4 Cubes and Cube Roots 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 m3. Find the side of the cube.
R.D. Sharma solutions for Mathematics [English] Class 8 4 Cubes and Cube Roots 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.
R.D. Sharma solutions for Mathematics [English] Class 8 4 Cubes and Cube Roots 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 cm3. Make use of the table for the cube root.
Solutions for 4: Cubes and Cube Roots
R.D. Sharma solutions for Mathematics [English] Class 8 chapter 4 - Cubes and Cube Roots
Shaalaa.com has the CBSE Mathematics Mathematics [English] Class 8 CBSE solutions in a manner that help students grasp basic concepts better and faster. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. R.D. Sharma solutions for Mathematics Mathematics [English] Class 8 CBSE 4 (Cubes and Cube Roots) include all questions with answers and detailed explanations. This will clear students' doubts about questions and improve their application skills while preparing for board exams.
Further, we at Shaalaa.com provide such solutions so students can prepare for written exams. R.D. Sharma textbook solutions can be a core help for self-study and provide excellent self-help guidance for students.
Concepts covered in Mathematics [English] Class 8 chapter 4 Cubes and Cube Roots are Concept of Cube Number, Concept of Cube Root, Cube Root Through Prime Factorisation Method, Finding the Cube Roots of the Cubic Numbers Through the Estimation Method, Patterns in Numbers.
Using R.D. Sharma Mathematics [English] Class 8 solutions Cubes and Cube Roots exercise by students is an easy way to prepare for the exams, as they involve solutions arranged chapter-wise and also page-wise. The questions involved in R.D. Sharma Solutions are essential questions that can be asked in the final exam. Maximum CBSE Mathematics [English] Class 8 students prefer R.D. Sharma Textbook Solutions to score more in exams.
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