RD Sharma solutions for Mathematics [English] Class 8 chapter 4 - Cubes and Cube Roots [Latest edition]

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'.

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

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?

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.

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 .

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.

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.

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.

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 .

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.