Important Questions for CBSE Class 8 Maths Chapter 6 - Cubes and Cube Roots

1. ${8^3} = $___\[ \times \]___\[ \times \]___

Ans: $8 \times 8 \times 8 = 512$

2. $( - 4) \times ( - 4) \times ( - 4) = ?$

Ans: $ - 4 \times  - 4 \times  - 4 =  - 64$

3. Say True/False. Is cube of every even number is even?

Ans: True

4. Say true/false. The cube of every odd number is not odd?

Ans:  False, cube of every odd number is odd.

5. ${(3.5)^3} = $ ?

Ans:  $3.5 \times 3.5 \times 3.5 = 12.25 \times 3.5 = 42.875$

6. ${x^3}$ is read as

Ans: $x$ to the power of \[3\] or $x$ cube.

7. $\sqrt[3]{{ - {x^3}}} = $ ?

Ans: $\sqrt[3]{{ - {x^3}}} =  - {\left( {{x^3}} \right)^{\dfrac{1}{3}}} =  - x$

8. $\sqrt[3]{{ab}} = ?$

Ans: $\sqrt[3]{a} \times \sqrt[3]{b}$

9. $\sqrt[3]{{\dfrac{a}{b}}} = ?$

Ans: $\dfrac{{\sqrt[3]{a}}}{{\sqrt[3]{b}}}$

10. A natural number is said to be __________ if it is the cube of some natural number.

Ans: Perfect cube

Short Answer Questions     2 Marks

11. Show that \[192\] is not a perfect cube.

Ans: By prime factorization,

$\sqrt[3]{{192}} = \sqrt[3]{{(2 \times 2 \times 2) \times (2 \times 2 \times 2) \times 3}}$

Here, the product cannot be expressed in the form of triplets. 

Hence, this is not a perfect cube.

12. Find the cube of $( - 9)$

Ans: ${( - 9)^3} =  - 9 \times  - 9 \times  - 9$

$ = 81 \times ( - 9)$

$ =  - 729$

13. Find the cube of \[2\dfrac{2}{3}\]

Ans: \[{\left( {2\dfrac{2}{3}} \right)^3} = 2\dfrac{2}{3} \times 2\dfrac{2}{3} \times 2\dfrac{2}{3}\]

$ = \dfrac{8}{3} \times \dfrac{8}{3} \times \dfrac{8}{3}$

$ = \dfrac{{512}}{{27}}$

14. Find the cube of $(0.09)$.

Ans: ${(0.09)^3} = 0.09 \times 0.09 \times 0.09$

$ = 0.0081 \times 0.09$

$ = 0.000729$

15. Show that \[4096\] is a perfect cube.

Ans: By prime factorization,

$\sqrt[3]{{4096}} = \sqrt[3]{{(2 \times 2 \times 2) \times (2 \times 2 \times 2) \times (2 \times 2 \times 2)\times (2 \times 2 \times 2)}}$

Here, the number can be expressed as the product of triplets. 

Hence, a given number is a perfect square.

16. By what least number should \[336\] be divided to get a perfect cube?

Ans: By prime factorization,

$\sqrt[3]{{336}} = \sqrt[3]{{(2 \times 2 \times 2) \times 2 \times 3 \times 7}}$

\[336\]should be divided by $2 \times 3 \times 7 = 42$.

17. By what least number should \[675\] multiplied to get a perfect cube?

Ans: By prime factorization,

$\sqrt[3]{{675}} = \sqrt[3]{{(3 \times 3 \times 3) \times 5 \times 5}}$

Hence to make it a perfect cube, we must multiply by \[5.\]

Long Answer Questions      4 Marks

18. What is the smallest number by which \[2048\] may be multiplied so that the product is a perfect cube?

Ans: By prime factorization,

\[\sqrt[3]{{2048}} = \sqrt[3]{{(2 \times 2 \times 2) \times (2 \times 2 \times 2) \times (2 \times 2 \times 2) \times 2 \times 2}}\]

Clearly \[2048\] should be multiplied with \[2\] to make perfect cube.

19. Find $\sqrt[3]{{125 \times ( - 343)}}$

Ans: By prime factorization

$ = \sqrt[3]{{5 \times 5 \times 5 \times ( - 7) \times ( - 7) \times ( - 7)}}$

$ = 5 \times ( - 7)$

$ =  - 35$

20. $\sqrt[3]{{\dfrac{{8000}}{{1331}}}}$

Ans: $\sqrt[3]{{\dfrac{{8000}}{{1331}}}}$ can be written as \[\dfrac{{\sqrt[3]{{8000}}}}{{\sqrt[3]{{1331}}}}\]

Calculate each value by prime factorization,

\[\sqrt[3]{{8000}} = \sqrt[3]{{(2 \times 2 \times 2) \times (5 \times 5 \times 5) \times (2 \times 2 \times 2)}}\]

\[\sqrt[3]{{1331}} = \sqrt[3]{{(11 \times 11 \times 11)}}\]

Now, 

$\sqrt[3]{{\dfrac{{8000}}{{1331}}}} = \sqrt[3]{{\dfrac{{2 \times 2 \times 2 \times 5 \times 5 \times 5 \times 2 \times 2 \times 2}}{{11 \times 11 \times 11}}}}$

$ = \dfrac{{2 \times 5 \times 2}}{{11}}$

$ = \dfrac{{20}}{{11}}$

Very Long Answer Questions      5 Marks

21. Find the value of ${31^3}$ by shortcut method.

Ans: Let ${(31)^3} = {(30 + 1)^3}$

We know, ${(a + b)^3} = {a^3} + 3{a^2}b + 3a{b^2} + {b^3}$

$(31){ = ^3}{(30 + 1)^3}$

$ = {(30)^3} + 3{(30)^2} + 3(30) + 1$

\[ = 27000 + (3 \times 900) + 90 + 1\]

\[ = 27000 + 2700 + 90 + 1\]

\[ = 29791\]

22. Evaluate $\sqrt[3]{{4913}}$

Ans: By prime factorization,

  $17|\underline {4913}$

  $17|\underline {289}$

  $17|\underline {17}$

$ = \sqrt[3]{{4913}}$

$ = \sqrt[3]{{17 \times 17 \times 17}}$

$ = 17$

23. Find $\sqrt[3]{{ - 13824}}$

Ans: By prime factorization,

$ - \sqrt[3]{{13824}} =  - \sqrt[3]{{(2 \times 2 \times 2) \times (2 \times 2 \times 2) \times (2 \times 2 \times 2) \times (3 \times 3 \times 3)}}$

$ =  - 2 \times 2 \times 2 \times 3$

$ =  - 4 \times 6$

$ =  - 24$ 

24. Evaluate $\sqrt[3]{{512 \times 343}}$

Ans: By prime factorization,

$\sqrt[3]{{512 \times 343}} = \sqrt[3]{{(2 \times 2 \times 2) \times (2 \times 2 \times 2) \times (2 \times 2 \times 2) \times (7 \times 7 \times 7)}}$

$ = 2 \times 2 \times 2 \times 7$

$ = 56$

Significance of CBSE Class 8 Maths Chapter 6 Cubes and Cube Roots Important Questions

Calculating cubes and cube roots requires following specific methods. There are important techniques explained by the CBSE Class 8 Maths Chapter 6 Cubes and Cube Roots. This chapter explains what a cube and the cube root of a number are and how to determine them. The mathematical operations explained in the chapter help students solve the exercise questions easily.

Once the exercises are completed, students can download and solve the important questions compiled by the experts of Vedantu. These questions are based on the latest CBSE syllabus of Class 8 Maths. The experts have covered all the important topics of this chapter while compiling these questions. Hence, these questions will act as the perfect guide to check the preparation level of the students.

The solutions provided with these important questions will also enable students to understand how to approach solving such questions. They will learn the precise stepwise methods to determine cubes and cube roots of different numbers and proceed with their preparation for this chapter.

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Download CBSE Class 8 Maths Chapter 6 Cubes and Cube Roots Important Questions PDF

Get the free PDF version of these questions and answers for this chapter. Solve these questions during your practice sessions and become better in this chapter. learn and imbibe the methods of determining cubes and cube roots faster to answer exam questions precisely and to stay ahead of the competition.

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