The least number by which 242 must be multiplied to make it a perfect square is

Class 8 Maths Chapter 7 Cubes and Cube Roots MCQs (Questions and Answers) are available online for students. These multiple-choice questions are designed by experts, according to the CBSE syllabus (2021-2022) and NCERT guidelines. The chapter-wise objective questions are given at BYJU’S to make each student learn each concept and lead them to score better marks in exams. Also, learn important questions for class 8 Maths here.

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Class 8 Maths Chapter 7 Cubes and Cube Roots MCQs Questions – Download PDF

MCQs on Class 8 Cubes and Cube Roots

Multiple choice questions (MCQs) are given for Class 8 Cubes and Cube Roots chapter. Each problem has four multiple options, in which one is the right answer. Students have to solve each problem and choose the correct answer.

1. The one’s digit of the cube of 53 is:

A. 9

B. 3

C. 7

D. 1

Answer: C

Explanation: 533 = 53 x 53 x 53

33 = 3x3x3 = 27

Hence, at the unit place, we will get 7.

Recheck: 533 = 53 x 53 x 53 = 148877

2. The prime factorisation of 64 is:

A. 2 x 2 x 2

B. 4 x 4 x 4

C. 8 x 8 x 8

D. None of the above

Answer: D

Explanation: 64 = 2 x 2 × 2 x 2 x 2 x 2 = 26

3. Which of the following is not a perfect cube?

A. 216

B. 1000

C. 243

D. 1331

Answer: C

Explanation: 243 = 3 × 3 × 3 × 3 × 3 = 33 × 32

4. By what number should 81 be divided to get a perfect cube?

A. 3

B. 6

C. 7

D. 9

Answer: A

Explanation: The prime factorisation of 81 will be:

81 = 3 × 3 × 3 × 3

81 = 33 × 3

Hence, we need to divide 81 by 3 to get:

81/3 = 27 = 33

5. By what number should we divide 135 to get a perfect cube?

A. 3

B. 5

C. 7

D. 9

Answer: B

Explanation: 135 = 3 x 3 x 3 x 5

We can see, 5 is the extra number which cannot be paired in a group of 3.

Hence, 135/5 = 27

6. Cube root of 512 is:

A. 4

B. 6

C. 8

D. 12

Answer: C

Explanation: By prime factorisation, we get:

512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

3√512 = 2 × 2 × 2 = 8

7. What should be divided by 53240 to make it a perfect cube?

A. 5

B. 10

C. 15

D. 20

Answer: A

Explanation: The prime factorisation of 53240

53240 = 2 × 2 × 2 × 11 × 11 × 11 × 5 = 23 × 113 × 5

Hence, we need to divide 53240 by 5

53240/5 = 10648 is a perfect cube.

8. The value of 43√1000 is:

A. 400

B. 40

C. 10

D. 4

Answer: B

Explanation: 43√1000 = 43√(10×10×10) = 4 × 10 = 40

9. A perfect cube of a number having 0 at its unit place, ends with _____ zeros.

A. 1

B. 2

C. 3

D. 4

Answer: C

Examples: 103 = 1000

203 = 8000

303 = 27000

10. Cube root of 15625 is:

A. 5

B. 15

C. 25

D. 35

Answer: C

Explanation: 15625 = 5 x 5 x 5 x 5 x 5 x 5

3√15625 = 5 × 5 = 25

11. Which of the following is a perfect cube?

A.125

B. 36

C. 75

D. 100

Answer: A. 125

Explanation:

125 = 5 × 5 × 5 = 5³

12. What is the cube of 2a?

A. 2a3

B. 4a3

C. 8a3

D. 16a3

Answer: C. 8a3

Explanation:

(2a)3 = 2a x 2a x 2a

= (2 x 2 x 2) x (a x a x a)

= 8a3

13. 1. The cube root of 13824 is __________.

A. 36

B. 25

C. 24

D. 16

Answer: C. 24

Explanation: Prime factorisation of 13824 is:

13824=2×2×2×2×2×2×2×2×2×3×3×3

13824=(2×2×2)×(2×2×2)×(2×2×2)×(3×3×3)

Taking cube root both the sides, we get;

(13824)⅓ = 2 x 2 x 2 x 3 = 24

14. Which of these numbers is not a cube number?

A. 10000

B. 343

C. 64

D. 729

Answer: A. 10000

Explanation: By prime factorisation method.

10000 = 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5.

= 24 × 54 = 2³ × 2 × 5³ × 5

Thus, the factors cannot be cubed.

15. When the square of a number is subtracted from the cube of the same number, it becomes 100. Find the number.

A.1

B. 2

C. 4

D. 5

Answer: D. 5

Explanation: Square of 5 = 5 x 5 = 25

Cube of 5 = 5 x5x5 = 125

125 – 25 = 100

16. Which is the smallest natural number by which 243 must be multiplied to make the product a perfect cube?

Solution:

(i) 243

Prime factors of 243 =

Here 3 do not appear in 3’s group.

Therefore, 243 must be multiplied by 3 to make it a perfect cube.

(ii) 256

Prime factors of 256 = 2\times2\times2\times2\times2\times2\times2\times2

Here one factor 2 is required to make a 3’s group.

Therefore, 256 must be multiplied by 2 to make it a perfect cube.

(iii) 72

Prime factors of 72 = 2\times2\times2\times3\times3

Here 3 does not appear in 3’s group.

Therefore, 72 must be multiplied by 3 to make it a perfect cube.

(iv) 675

Prime factors of 675 = 3\times3\times3\times5\times5

Here factor 5 does not appear in 3’s group.

Therefore 675 must be multiplied by 3 to make it a perfect cube.

(v) 100

Prime factors of 100 = 2\times2\times5\times5

Here factor 2 and 5 both do not appear in 3’s group.

Therefore 100 must be multiplied by 2\times5= 10 to make it a perfect cube.

What is the perfect square of 242?

What number should be multiplied by 252 to make it a perfect square?

What should be multiplied to 243 to make it a perfect square?

Does 252 make a perfect square?