This set of Mathematics Written Test Questions and Answers for Class 8 focuses on “Smallest Number which is a Perfect Cube”.

1. Which of the following numbers is a perfect cube?

a) 7

b) 9

c) 8

d) 2

View Answer

Explanation: Perfect cube is formed when a natural number is multiplied to itself thrice. When 2 is multiplied with itself thrice, we get 8. Thus, 8 is a perfect cube. None of the other options can be obtained by multiplying a natural number with itself thrice.

2. Which of the following numbers is not a perfect cube?

a) 729

b) 216

c) 8

d) 2

View Answer

Explanation: Perfect cube is formed when a natural number is multiplied to itself thrice. When 9 is multiplied with itself thrice, we get 729. When 6 is multiplied with itself thrice, we get 216. When 2 is multiplied with itself thrice, we get 8. Thus, 729, 216 and 8 are a perfect cube. 2 cannot be obtained by multiplying any natural number with itself thrice. Hence, 2 is not a perfect cube.

3. Which of the following numbers is a perfect cube?

a) 1331

b) 91

c) 98

d) 21

View Answer

Explanation: Perfect cube is formed when a natural number is multiplied to itself thrice. When 11 is multiplied with itself thrice, we get 1331. Thus, 1331 is a perfect cube. None of the other options can be obtained by multiplying a natural number with itself thrice.

4. Which of the following numbers is a square and perfect cube?

a) 72

b) 125

c) 64

d) 100

View Answer

Explanation: 8 multiplied to itself gives us 64. Thus, 64 is a square. Perfect cube is formed when a natural number is multiplied to itself thrice. When 4 is multiplied with itself thrice, we get 64. Thus, 64 is a perfect cube. Thus, 64 is square and perfect cube. None of the other options are square and perfect cube.

5. Find the smallest natural number by which 243 must be multiplied so that the product is a perfect cube.

a) 3

b) 4

c) 5

d) 6

View Answer

Explanation: Perfect cube is formed when a natural number is multiplied to itself thrice. Factorizing 243 we get:

243 = 3×3×3×3×3

When 243 is multiplied with 3, we get 729 which is a perfect cube.

6. Find the smallest natural number by which 4394 must be multiplied so that the product is a perfect cube.

a) 3

b) 2

c) 5

d) 7

View Answer

Explanation: Perfect cube is formed when a natural number is multiplied to itself thrice. Factorizing 4394 we get:

4394 = 2×2×13×13×13

When 4394 is multiplied with 2, we get 17576 which is 26

^{3}. Thus, 17576 is a perfect cube.

7. Find the smallest natural number by which 49000 must be multiplied so that the product is a perfect cube.

a) 3

b) 2

c) 5

d) 7

View Answer

Explanation: Perfect cube is formed when a natural number is multiplied to itself thrice. Factorizing 49000 we get:

49000 = 2×2×2×5×5×5×7×7

When 49000 is multiplied with 7, we get 343000 which is 70

^{3}. Thus, 343000 is a perfect cube.

8. Find the smallest natural number by which 265837 must be multiplied so that the product is a perfect cube.

a) 11

b) 2

c) 5

d) 7

View Answer

Explanation: Perfect cube is formed when a natural number is multiplied to itself thrice. Factorizing 265837 we get:

265837 = 13×13×13×11×11

When 265837 is multiplied with 11, we get 2924207 which is 143

^{3}. Thus, 2924207 is a perfect cube.

9. Find the smallest natural number by which 6125 must be multiplied so that the product is a perfect cube.

a) 3

b) 2

c) 5

d) 7

View Answer

Explanation: Perfect cube is formed when a natural number is multiplied to itself thrice. Factorizing 6125 we get:

6125 = 5×5×5×7×7

When 6125 is multiplied with 7, we get 42875 which is 35

^{3}. Thus, 42875 is a perfect cube.

10. Find the smallest natural number by which 19652 must be multiplied so that the product is a perfect cube.

a) 3

b) 2

c) 5

d) 7

View Answer

Explanation: Perfect cube is formed when a natural number is multiplied to itself thrice. Factorizing 19652 we get:

19652 = 2×2×19×19×19

When 19652 is multiplied with 2, we get 39304 which is 38

^{3}. Thus, 39304 is a perfect cube.

**Sanfoundry Global Education & Learning Series – Mathematics – Class 8**.

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