Cubes and Cube Roots Test

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Cubes and Cube Roots Test - 1

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following is the smallest number that must be multiplied with 4500 to form a perfect cube?

A
2

B
3

C
6

D
8

Solution

4500 = 2 × 2 × 3 × 3 × 5 × 5 × 5
The factors have three 5's, only two 2's and two 3's.
So, to make triplets of 2's and 3's, we need one 2 and one 3 more.
So, to make a perfect cube, we should multiply the given number by 2 × 3 = 6.
Question 2
1 / -0

Anuj wants to make a cube. He has a cuboid of dimensions 3 cm × 2 cm × 3 cm. How many such cuboids will he need to form a cube?

A
12

B
20

C
6

D
24

Solution

To make triplets, he needs 3 × 2 × 2 = 12 cuboids.
So, 12 cuboids are needed.
Question 3
1 / -0

Which of the following statements is/are true?

(i) 6 should be multiplied with 182 to make it a perfect cube.
(ii) 5 should be multiplied with 235 to make it a perfect cube.

A
Both (i) and (ii) are true.

B
Only (i) is true.

C
Only (ii) is true.

D
Both (i) and (ii) are false.

Solution

(i) 182 = 2 × 13 × 7
To make it a perfect cube, we don't need 6.

(ii) 235 = 5 × 47
To make it a perfect cube, we need two 5s and two 47s.

Hence, both (i) and (ii) are false.
Question 4
1 / -0

Which of the following is true?

A
2^{2 ×}3^{3 ×}13³ must be divided by 2 to make the quotient a perfect cube.

B
2² ×3^{3 ×}13³ must be multiplied by 2² to make the product a perfect cube.

C
2 must be multiplied by the factors of 2744 to make it a perfect cube.

D
2^{2 ×}3^{2 ×}13^{3 ×}17³ must be divided by 36 to make the quotient a perfect cube.

Solution

2^{2 ×}3^{2 ×}13^{3 ×}17³

As 2 and 3 are not grouped in triplets, so it must be divided by 2^{2 ×}3² = 36 to make quotient a perfect cube.
Question 5
1 / -0

What is the unit digit of (23173)³ + (743129)³?

A
9

B
7

C
2

D
6

Solution

Unit digit of (23173)³ = Unit digit of 3³ = 7
Unit digit of (743129)³ = Unit digit of 9³ = 9
Adding unit digits,
7 + 9 = 16
∴ The unit digit of (23173)³ + (743129)³= 6
Question 6
1 / -0

The cube of an even natural number is always

A
even

B
odd

C
even or odd

D
can't say

Solution

The cube of an even natural number is always even.
For example:
Cube of 2 = 2 × 2 × 2 = 8
Cube of 4 = 4 × 4 × 4 = 64
Cube of 6 = 6 × 6 × 6 = 216 and so on.
Question 7
1 / -0

Which of the following is the smallest perfect odd cube between 1700 to 5000?

A
1727

B
2197

C
1731

D
4913

Solution

12³ = 1728
13³ = 2197
14³ = 2744
15³ = 3375
16³ = 4096
17³ = 4913

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Re-Attempt Weekly Quiz Competition

Cubes and Cube Roots Test - 1

Result

Cubes and Cube Roots Test - 1

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SHARING IS CARING

Question 1

2

3

6

8

Solution

Question 2

12

20

6

24

Solution

Question 3

Both (i) and (ii) are true.

Only (i) is true.

Only (ii) is true.

Both (i) and (ii) are false.

Solution

Question 4

22 × 33 × 133 must be divided by 2 to make the quotient a perfect cube.

22 × 33 × 133 must be multiplied by 22 to make the product a perfect cube.

2 must be multiplied by the factors of 2744 to make it a perfect cube.

22 × 32 × 133 × 173 must be divided by 36 to make the quotient a perfect cube.

Solution

Question 5

9

7

2

6

Solution

Question 6

even

odd

even or odd

can't say

Solution

Question 7

1727

2197

1731

4913

Solution

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Question Analysis

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2^{2 ×}3^{3 ×}13³ must be divided by 2 to make the quotient a perfect cube.

2² ×3^{3 ×}13³ must be multiplied by 2² to make the product a perfect cube.

2^{2 ×}3^{2 ×}13^{3 ×}17³ must be divided by 36 to make the quotient a perfect cube.