Worksheet on Cube and Cube Root is the best source to begin your math practice. All the Cube and Cube Root problems are provided here to help the students learn math. Simply check and verify the process of explanation and try on your own to get complete knowledge on Cube and Cube Root Worksheets Problems. Know how to find a Cube Root of Number in the simplest way by referring to our Worksheet for Cube and Cube Root.

Students must include Cube and Cube Root Worksheets while practicing. You can check the multiple-choice questions, practice questions, and also sample examples in our Cube and Cube Root Practice Sheet. Take the better move to learn the Cube and Cube Root Math Problems by referring to our worksheets. All type of problems are clearly explained with the step by step process.

1. Find which of the following numbers is a perfect cube?

(a) 256

(b) 81

(c) 2744

(d) 16

## Solution:

(a) 256

Find the Prime Factors of the given number 256

256 prime factors are 4, 4, 4, 4

256 = 4 × 4 × 4 × 4

Form the triplets with the group of the same prime factor numbers.

256 = (4 × 4 × 4) × 4

There is only one triplet and one single factor available.

Therefore, the given number is not a perfect cube.

(b) 81

Find the Prime Factors of the given number 81

81 prime factors are 3, 3, 3, 3

81 = 3 × 3 × 3 × 3

Form the triplets with the group of the same prime factor numbers.

81 = (3 × 3 × 3) × 3

There is only one triplet and one single factor available.

Therefore, the given number is not a perfect cube.

(c) 2744

Find the Prime Factors of the given number 2744

2744 prime factors are 14, 14, 14

2744 = 14 × 14 × 14

Form the triplets with the group of the same prime factor numbers.

2744 = (14 × 14 × 14)

There is only one triplet available

(d) 16

Find the Prime Factors of the given number 16

16 prime factors are 2, 2, 2, 2

16 = 2 × 2 × 2 × 2

Form the triplets with the group of the same prime factor numbers.

16 = (2 × 2 × 2) × 2

There is only one triplet and one single factor available.

Therefore, the given number is not a perfect cube.

Therefore, (c) 2744 is a perfect cube.

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

(a) 1331

(b) 729

(c) 4096

(d) 2744

## Solution:

(a) 1331

Find the Prime Factors of the given number 1331

1331 prime factors are 11, 11, 11

1331 = 11 × 11 × 11

Form the triplets with the group of the same prime factor numbers.

1331 = (11 × 11 × 11)

There is only one triplet available.

Therefore, the given number is a perfect cube.

(b) 729

Find the Prime Factors of the given number 729

729 prime factors are 9, 9, 9

729 = 9 × 9 × 9

Form the triplets with the group of the same prime factor numbers.

729 = (9 × 9 × 9)

There is only one triplet available.

Therefore, the given number is a perfect cube.

(c) 4096

Find the Prime Factors of the given number 4096

4096 prime factors are 8, 8, 8, 8

4096 = 8 × 8 × 8 × 8

Form the triplets with the group of the same prime factor numbers.

4096 = (8 × 8 × 8) × 8

There is only one triplet and one single factor available.

Therefore, the given number is not a perfect cube.

(d) 2744

Find the Prime Factors of the given number 2744

2744 prime factors are 14, 14, 14

2744 = 14 × 14 × 14

Form the triplets with the group of the same prime factor numbers.

2744 = (14 × 14 × 14)

There is only one triplet available.

Therefore, the given number is a perfect cube.

(c) 4096 is not a perfect cube.

3. What least number must be multiplied to 8575 so that the product becomes a perfect cube?

(a) 4

(b) 2

(c) 7

(d) 5

## Solution:

Find the Prime Factors of the given number 8575

8575 prime factors are 7, 7, 7, 5, 5

8575 = 7 × 7 × 7 × 5 × 5

Form the triplets with the group of the same prime factor numbers.

8575 = (7 × 7 × 7) × (5 × 5)

Multiply 5 to the given number to make it a perfect cube.

4. What is the least number by which 12096 must be divided so that the quotient is a perfect cube?

(a) 5

(b) 7

(c) 3

(d) 4

## Solution:

Find the Prime Factors of the given number 12096

12096 prime factors are 12, 12, 12, 7

12096 = 12 × 12 × 12 × 7

Form the triplets with the group of the same prime factor numbers.

12096 = (12 × 12 × 12) × 7

Divide 7 to the given number to make it a perfect cube.

5. ∛4913

(a) 18

(b) 21

(c) 14

(d) 17

## Solution:

Write the product of primes of a given number 4913 those form groups in triplets.

Cube Root of 4913 = ∛4913 = ∛(17 ×17 × 17)

Take one number from a group of triplets to find the cube root of 4913.

Therefore, 17 is the cube root of a given number 4913.

(d) 17 is the cube root of 4913

6. Evaluate: ∛[(2197)/216]

(a) 6/13

(b) 12/11

(c) 11/12

(d) 13/6

## Solution:

Firstly, apply the cube root to both integers.

∛(a/b) = (∛a)/(∛b)

∛(2197/216) = ∛2197/∛216

Then, find the prime factors for each integer separately.

[∛(13 × 13 × 13)]/[ ∛(6 × 6 × 6)]

Take each integer from the group in triplets to get the cube root of a given number.

13/6

13/6 is the cube root of ∛(2197/216).