Cubes and Cube Roots MCQs

Ans: a) 125

Explanation: When a number is multiplied by itself 2 times, the result is known as the cube of the number. 

The factors of 125 = 5 × 5 × 5

The factors of 36 = 2 × 2 × 3 × 3

The factors of 75 = 5 × 5 × 3

The factors of 100 = 2 × 2 × 5 × 5

Hence we can infer that 125 is a cube of 5 and the remaining numbers are not cubes as they do not have factors that repeat 3 times.

Ans: d) 10000 

Explanation: When a number is multiplied by itself twice then the result obtained is called the cube of the number.

Here, the factors of 1331 = 11 × 11 × 11 = 11³. 

⇒1331 is a cube number.

The factors of 125 = 5 × 5 × 5 = 5³

⇒125 is a cube number.

The factors of 729 = 9 × 9 × 9 = 9³

⇒ 729 is a cube number.

The factors of 10000 = 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5 = 2⁴ × 5⁴ which is not a cube.

⇒ 10000 is not a cube number.

Hence the answer is d.

Ans: c) 3

Explanation: 47³ = 47 × 47 × 47

⇒ 7³ = 7 × 7 × 7 = 343

Hence, for any number ending with 7, the digit in the unit’s place will be 3.

We can verify the same by finding 47³ = 47 × 47 × 47 which is equal to 103823.

Ans: b) 5

Explanation: The prime factors of 625 = 5 × 5 × 5 × 5

⇒ 625 = 5?

⇒ 625 = 5³ × 5

⇒ 625/5 = 5³

Hence, to get a perfect cube, we should divide the number 625 by 5.

Hence, the answer is b.

Ans: c) 17

Explanation: The prime factors of 4913 = 17 × 17 × 17 = 17³

As the inverse is the cube root of the number, we can say that \(\sqrt [3] { }\)4913 = \(\sqrt [3] { }\)17³ = 17

Hence, the answer is c.

Ans: d) 4

Explanation: 

We know that 4 × 4 × 4 = 64 which means the number in the one’s place of the cube root of 2744 must be 4.

The prime factors of 2744 = 2 × 2 × 2 × 7 × 7 × 7 = 2³ × 7³

To recheck it, \(\sqrt [3] { }\)2744 = \(\sqrt [3] { }\)2³ × 7³ = 2 × 7 = 14

Hence the answer is d.

Ans: d) 5

Explanation: Let us verify the condition mentioned in the Question for all the options given. 

1. 2³ - 2² = 8 - 4 = 4. Hence the condition is not satisfied.
2. 4³ - 4² = 64 - 16 = 48. Hence the condition is not satisfied.
3. 1³ - 1² = 1 - 1 = 0. Hence the condition is not satisfied.
4. 5³ - 5² = 125 - 25 = 100. Here, the condition is satisfied.

Hence, the answer is d.

Ans: c) 24

Explanation: The prime factors of 13824 are 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)

⇒ 13824 = 2³ × 2³ × 2³ × 3³

⇒ \(\sqrt [3] { }\)13824 = \(\sqrt [3] { }\)2³ × 2³ × 2³ × 3³ = 2 × 2 × 2 × 3 = 24

Hence the cube root of 13824 is 24.

Hence the answer is c.

Ans: b) 40 

Explanation: The prime factors of 1000 = 2 × 2 × 2 × 5 × 5 × 5

⇒ 1000 = (2 × 2 × 2) × (5 × 5 × 5)

⇒ 1000 = 2³ × 5³

⇒ \(\sqrt [3] { }\)1000 = \(\sqrt [3] { }\)(2³ × 5³)

⇒ \(\sqrt [3] { }\)1000 = 2 × 5 = 10

⇒ 4\(\sqrt [3] { }\)1000 = 4 × 10 = 40

Hence, 4\(\sqrt [3] { }\)1000 = 40

Hence, the answer is b.

Ans: b) 2

Explanation: The number of zeros in the cube number 8000000 is 6.

\(\sqrt [3] { }\)8000000 = \(\sqrt [3] { }\)2³ × 100³ = 2 × 100 = 200

Hence the number of zeros in the cube root of 8000000 is 2.

Hence the answer is b.

Ans: c) 3

Explanation: The prime factors of 72 = 2 × 2 × 2 × 3 × 3

⇒ 72 = 2³ × 3 × 3

So, we can infer that if 72 is multiplied by a 3, it will become a perfect cube number.

Hence, the answer is c.

Ans: a) 11

Explanation: The prime factors of 88 = 2 × 2 × 2 × 11

⇒ 88 = 2³ × 11

⇒ 88/11 = 2³

Hence, the smallest number by which 88 should be divided to get a perfect cube is 11.

Hence, the answer is a.

Ans: c) 8

Explanation: The digit in the one’s place of the number 5022 is 2.

⇒ The digit in the one’s place of the cube number will be 2 × 2 × 2 = 8.

If we recheck it, 5022³ = 5022 × 5022 × 5022 = 126657270648.

Hence, the answer is c.

Ans: d) 8a³

Explanation: The cube of 2a can be expressed as 2a × 2a × 2a which is equal to (2a)³

(2a)³ = 2³ × a³ = 8a³.

Hence the answer is d.

Ans: c) 15625

Explanation: 

The prime factors of 400 = 2 × 2 × 2 × 2 × 5 × 5 = 2? × 5²

⇒ 400 is not a perfect cube

The prime factors of 2025 = 5 × 5 × 3 × 3 = 5² × 3²

⇒ 2025 is not a perfect cube

The prime factors of 15625 = 5 × 5 × 5 × 5 × 5 × 5 = 5³ × 5³

⇒15625 is a perfect cube and its cube root is 25.

The prime factors of 9000 = 3 × 3 × 5 × 5 × 5 × 2 × 2 × 2 = 3² × 5³ × 2³

⇒ 9000 is not a perfect cube

Hence the answer is c.