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

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$

5 Important Formulas from Class 8 Maths Chapter 6 Cubes and Cube Roots

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

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Conclusion

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