MCQ about Cube Root

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?
A. 3
B. 9
C. 8
D. 7
Answer: A. 3
Explanation: 243 x 3 = 729
Hence, by prime factorisation of 729 we get;
729 = 3 x 3 x 3 x 3 x 3 x 3
729 = 33 x 33
Taking cube root on both the sides, we get;
(729)⅓ = 3 x 3 = 9
17. The one’s digit of the cube of the number 111 is:
A. 1
B. 2
C. 3
D. 9
Answer: A. 1
Explanation: The unit place of 111 has 1.
Cube of 1 = 13 = 1 x 1 x 1 = 1
18. The cube of 23 is:
A. 2304
B. 12167
C. 529
D. 23
Answer: B. 12167
Explanation: Cube of 23 = 23 x 23 x 23 = 12167
19. The one’s digit of the cube of the number 242 is
A. 2
B. 4
C. 6
D. 8
Answer: D. 8
Explanation: The unit digit of 242 is 2.
Cube of 2 = 2 x 2 x 2 = 8
20. Find the smallest number by which the number 200 must be multiplied to obtain a perfect cube.
A. 2
B. 10
C. 5
D. 100
Answer: C. 5
Explanation: The prime factorisation of 200 gives:
200 = 2 × 2 × 2 × 5 × 5 = 2³ × 5 × 5
Now multiply by 5 on both sides.
200 x 5 = 2³ × 53
(1000)1/3 = 2 × 5 = 10
1. Which of the following is correct?
I. Cube of a negative number is always positive.
II. Cube of a negative number is always negative.
III. Cube of a negative number may be positive or negative.
IV. All of the above
2. If the digit in one’s place of a number is 2, then the last digit of its cube will be:
I. 2
II. 4
III. 6
IV. 8
3. If the digit in one’s place of a number is 3, then the last digit of its cube will be:
I. 3
II. 6
 III. 7
IV. 9
4. If the digit in one’s place of a number is 6, then the last digit of its cube will be:
I. 6
II. 3
III. 2
IV. 8
5. The volume of a cubical box is 64 cm3. Which of the following is its side?
I. 2 cm
II. 4 cm
III. 6 cm
IV. 8 cm
6. Which of the following is a perfect cube?
I. 10000
II. 243
III. 343
IV. 270000
7. If a number is doubled then which of the following is a correct statement?
I. Its cube is two times the cube of the given number.
II. Its cube is three times the cube of the given number.
III. Its cube is six times the cube of the given number.
IV. Its cube is eight times the cube of the given number.
8. Which of the following is equal to its own cube?
I. -1
II. -2
III. -3
IV. -9
9. Which of the following is the cube root of 27000?
I. 30
II. 300
III. 3000
IV. None of these
10. Which of the following is the cube root of -64/243?
I. 7/4
II. -7/4
III. 4/7
IV. -4/7
ANSWERS
1. II
2. IV
3. III
4. I
5. II
6. III
7. IV
8. I
9. I
10. IV
Question 1. Which of the following numbers is a perfect cube ?
(a) 125
(b) 36
(c) 75
(d) 100.

Answer: (a) Hint: 125 = 5 × 5 × 5 = 5³.

Question 2. Which of the following numbers is a cube number ?

(a) 1000
(b) 400
(c) 100
(d) 600.

Answer: (a) Hint: 1000 = 10 × 10 × 10 = 10³.

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

(a) 1331
(b) 512
(c) 343
(d) 100.

Answer: (d) Hint: 100 = 2 × 2 × 5 × 5 = 2² × 5².

Question 4. Which of the following numbers is not a cube number ?

(a) 10000
(b) 3125
(c) 64
(d) 729.

Answer: (a) Hint: 10000 = 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5.

= 24 × 54 = 2³ × 2 × 5³ × 5.

Question 5 The cube of an odd natural number is

(a) even
(b) odd
(c) may be even, may be odd
(d) prime number.
Answer: (b) Hint: 3 × 3 × 3 = 27 (odd).

Question 6. The cube of an even natural number is

(a) even
(b) odd
(c) may be even, may be odd
(d) prime number.

Answer: (a) Hint: 6 × 6 × 6 = 216 (even).

Question 7. The one’s digit of the cube of the number 111 is

(a) 1
(b) 2
(c) 3
(d) 9.

Answer: (a) Hint: 1 × 1 × 1 = 1.

Question 8. The one’s digit of the cube of the number 242 is

(a) 2
(b) 4
(c) 6
(d) 8.

Answer: (d) Hint: 2 × 2 × 2 = 8.

Question 9. The one’s digit of the cube of the number 123 is

(a) 3
(b) 6
(c) 9
(d) 7.

Answer: (d) Hint: 3 × 3 × 3 = 27.

Question 10. The one’s digit of the cube of the number 144 is
(a) 1
(b) 2
(c) 3
(d) 4.

Answer: (d) Hint: 4 × 4 × 4 = 64.

Question 11. The one’s digit of the cube of the number 50 is

(a) 1
(b) 0
(c) 5
(d) 4.

Answer: (b) Hint: 0 × 0 × 0 = 0.

Question 12. The one’s digit of the cube of the number 326 is
(a) 2
(b) 3
(c) 6
(d) 4.

Answer: (c) Hint: 6 × 6 × 6 = 216.

Question 13. The one’s digit of the cube of the number 325 is
(a) 2
(b) 5
(c) 3
(d) 6.

Answer: (b) Hint: 5 × 5 × 5 = 125.

Question 14. The one’s digit of the cube of the number 347 is
(a) 3
(b) 4
(c) 7
(d) 1.

Answer: (a) Hint: 7 × 7 × 7 = 343.

Question 15. The one’s digit of the cube of the number 68 is
(a) 1
(b) 2
(c) 6
(d) 8.

Answer: (b) Hint: 8 × 8 × 8 = 512.

Question 16. The one’s digit of the cube of the number 249 is
(a) 2
(b) 4
(c) 9
(d) 1.

Answer: (c) Hint: 9 × 9 × 9 = 729.

Question 17. What is the one’s digit in the cube root of the cube number 1331 ?
(a) 1
(b) 2
(c) 3
(d) 4

Answer: (a) Hint: 1 × 1 × 1 = 1.

Question 18. What is the one’s digit in the cube root of the cube number 1000000 ?
(a) 0
(b) 1
(c) 2
(d) 9.

Answer: (a) Hint: 0 × 0 × 0 = 0.

Question 19. What is the one’s digit in the cube root of the cube number 1728 ?
(a) 1
(b) 2
(c) 3
(d) 9.
Answer: (b) Hint: 2 × 2 × 2 = 8.

Question 20. What is the one’s digit in the cube root of the cube number 2197 ?
(a) 1
(b) 2
(c) 3
(d) 7.

Answer: (c) Hint: 3 × 3 × 3 = 27.

Question 21. What is the one’s digit in the cube root of the cube number 2744 ?
(a) 1
(b) 2
(c) 3
(d) 4.

Answer: (d)Hint: 4 × 4 × 4 = 64.

Question 22. What is the one’s digit in the cube root of the cube number 3375 ?
(a) 2
(b) 3
(c) 5
(d) 4.

Answer: (c) Hint: 5 × 5 × 5 = 125

Question 23. What is the one’s digit in the cube root of the cube number 4096 ?
(a) 2
(b) 6
(c) 4
(d) 9.

Answer: (b) Hint: 6 × 6 × 6 = 216.

Question 24. What is the one’s digit in the cube root of the cube number 4913 ?
(a) 7
(b) 9
(c) 3
(d) 6.
Answer: (a) Hint: 7 × 7 × 7 = 343.

Question 25. What is the one’s digit in the cube root of the cube number 5832 ?
(a) 2
(b) 4
(c) 6
(d) 8.

Answer: (d) Hint: 8 × 8 × 8 = 512.

Question 26. What is the one’s digit in the cube root of the cube number 6859 ?
(a) 7
(b) 8
(c) 9
(d) 6.

Answer: (c) Hint: 9 × 9 × 9 = 729.

Question 27. What is the one’s digit in the cube root of the cube number 8000 ?
(a) 0
(b) 2
(c) 4
(d) 8.

Answer: (a) Hint: 0 × 0 × 0 = 0.

Question 28. The number of zeroes at the end of the cube of the number 20 is
(a) 1
(b) 2
(c) 3
(d) 6.

Answer: (c) Hint: ∵ Number of zeroes at the end of the number 20 = 1

∴ Number of zeroes at the end of its cube = 3 × 1 = 3.

Question 29. The number of zeroes at the end of the cube root of the cube number 1000
is
(a) 1
(b) 2
(c) 3
(d) 4.

Answer: (a) Hint: ∵ Number of zeroes at the end of the cube = 3

∴ Number of zeroes at the end of the cube root = \(\frac{3}{3}\) = 1.

Question 30. The number of zeroes at the end of the cube of the number 100 is
(a) 1
(b) 2
(c) 4
(d) 6.

Answer: (d) Hint: ∵ Number of zeroes at the end of the number 100 = 2
∴ Number of zeroes at the end of its cube = 3 × 2 = 6.

Question 31. The number of zeroes at the end of the cube root of the cube number
8000000 is
(a) 1
(b) 2
(c) 3
(d) 6.

Answer: (b) Hint: ∵ Number of zeroes at the end of the cube = 6

∴ Number of zeroes at the end of the cube root = \(\frac{6}{3}\) = 2.

Question 32. Find the smallest number by which the number 108 must be multiplied to
obtain a perfect cube.
(a) 2
(b) 3
(c) 4
(d) 5.

Answer: (a) Hint: 108 = 2 × 2 × 3 × 3 × 3 = 2 × 2 × 3³.

Question 33. Find the smallest number by which the number 250 must be divided to
obtain a perfect cube.
(o) 2
(b) 3
(c) 4
(d) 5.

Answer: (a) Hint: 250 = 5 × 5 × 5 × 2 = 5³ × 2.

Question 34. Find the smallest number by which the number 72 must be multiplied to
obtain a perfect cube.
(a) 2
(b) 3
(c) 4
(d) 6.

Answer: (b) Hint: 72 = 2 × 2 × 2 × 3 × 3 = 2³ × 3 × 3.

Question 35. Find the smallest number by which the number 375 must be divided to
obtain a perfect cube.
(a) 2
(b) 3
(c) 5
(d) 4.

Answer: (b) Hint: 375 = 3 × 5 × 5 × 5 = 3 × 5³.

Question 36.
Find the smallest number by which the number 100 must be multiplied to obtain a
perfect cube.
(a) 5
(b) 2
(c) 4
(d) 10.

Answer: (d) Hint: 100 = 2 × 2 × 5 × 5.

Question 37. Find the smallest number by which the number 10000 must be divided to
obtain a perfect cube.
(a) 2
(b) 5
(c) 10
(d) 100
Answer: (c) Hint: 10000 = 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5
= 2³ × 2 × 5³ × 5.

Question 38. Find the smallest number by which the number 200 must be multiplied to
obtain a perfect cube.
(a) 2
(b) 10
(c) 5
(d) 100.

Answer: (c) Hint: 200 = 2 × 2 × 2 × 5 × 5 = 2³ × 5 × 5.

Question 39. Find the smallest number by which the number 625 must be divided to
obtain a perfect cube.
(a) 3
(b) 5
(c) 25
(d) 125.

Answer: (b) Hint: 625 = 5 × 5 × 5 × 5 = 5³ × 5.

Question 40. Find the smallest number by which the number 128 must be multiplied to
obtain a perfect cube.
(a) 2
(b)4
(c) 3
(d) 8.

Answer: (b) Hint: 128 = 2 × 2 × 2 × 2 × 2 × 2 × 2

= 2³ × 2³ × 2.

Question 41. Find the smallest number by which the number 256 must be divided to
obtain a perfect cube.
(a) 2
(b) 4
(c) 8
(d) 16.
Answer: (b) Hint: 256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
= 2³ × 2³ × 2 × 2.

Question 42. Find the smallest number by which the number 36 must be multiphed to
obtain a perfect cube.
(a) 6
(b) 2
(c) 3
(d) 4.

Answer: (a) Hint: 36 = 2 × 2 × 3 × 3.

Question 43. Find the smallest number by which the number 1296 must be divided to
obtain a perfect cube.
(a) 6
(b) 2
(c) 4
(d) 3.

Answer: (a) Hint: 1296 =2 × 2 × 2 × 2 × 3 × 3 × 3 × 3

= 2³ × 2 × 3³ × 3.

Question 44. Find the smallest number by which the number 392 must be multiplied to
obtain a perfect cube.
(a) 3
(b) 5
(c) 7
(d) 6.

Answer: (c) Hint: 392 = 2 × 2 × 2 × 7 × 7 = 2³ × 7 × 7

Question 45. Find the smallest number by which the number 2401 must be divided to
obtain a perfect cube.
(a) 7
(b) 6
(c) 5
(d) 9.
Answer: (a) Hint: 2401 = 7 × 7 × 7 × 7 = 7³ × 7.

Question 46. Find the smallest number by which the number 121 must be multiplied to
obtain a perfect cube.
(a) 7
(b) 9
(c) 11
(d) 5.

Answer: (c) Hint: 121 = 11 × 11.

Question 47. Find the smallest number by which the number 88 must be divided to
obtain a perfect cube.
(a) 11
(b) 5
(c) 7
(d) 9.

Answer: (a) Hint: 88 = 2 × 2 × 2 × 11 = 2³ × 11.

Question 48. The volume of a cube is 64 cm³. The edge of the cube is
(a) 4 cm
(b) 8 cm
(c) 16 cm
(d) 6 cm.

Answer: (a) Hint: Edge = \(\sqrt[3]{64}\) = \(\sqrt[3]{2 × 2 × 2 × 2 × 2 × 2}\)

= \(\sqrt[3]{2^3×2^3}\) = 2 × 2 = 4.
Question 49. Apala makes a cuboid of plasticine of sides 5 cm, 4 cm, 2 cm. How many
such cuboids will be needed to form a cube ?
(a) 20
(b) 25
(c) 10
(d) 16.

Answer: (b) Hint: Volume = 5 × 4 × 2 = 5 × 2 × 2 × 2= 5 × 2³.

Question 50. Which of the following is false ?
(a) Cube of any odd number is odd
(b) A perfect cube does not end with two zeroes
(c) The cube of a single digit number may be a single digit number
(d) There is no perfect cube which ends with 8.

Answer: (d) Hint:1728 = 12³.

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

a. 125
b. 36
c. 75
d. 100

Click here for the answer

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.

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

a. 1331
b. 125
c. 729
d. 10000

Click here for the answer

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.

Question 3. Which of the following is the one’s digit of the cube of 47?

a. 2
b. 1
c. 3
d. 9

Click here for the answer

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.

Question 4. To get a perfect cube, by which number should we divide 625?

a. 2
b. 5
c. 7
d. 3

Click here for the answer

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.

Question 5. Which of the following is the cube root of 4913?

a. 23
b. 13
c. 17
d. 21

Click here for the answer

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 3√34913 = 3√317³ = 17

Hence, the answer is c.

Question 6. What is the one’s digit in the cube root of 2744?

a. 1
b. 2
c. 5
d. 4

Click here for the answer

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, 3√32744 = 3√323 × 73 = 2 × 7 = 14

Hence the answer is d.

Question 7. When the square of a number is subtracted from the cube of the
same number, the result is 100. Find the number from the ones given below.

a. 2
b. 4
c. 1
d. 5

Click here for the answer

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.

Question 8. Which of the following is the cube root of 13824?

a. 36
b. 25
c. 24
d. 18

Click here for the answer

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
⇒ 3√313824 = 3√323 × 23 × 23 × 33 = 2 × 2 × 2 × 3 = 24

Hence the cube root of 13824 is 24.

Hence the answer is c.

Question 9. What is the value of 43√31000?

a. 4
b. 40
c. 400
d. 100

Click here for the answer

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

⇒ 3√31000 = 3√3(23 × 53)

⇒ 3√31000 = 2 × 5 = 10

⇒ 43√31000 = 4 × 10 = 40

Hence, 43√31000 = 40

Hence, the answer is b.

Question 10. How many zeros will be there in the cube root of the number
8000000?

a. 6
b. 2
c. 1
d. 3

Click here for the answer

Ans: b) 2

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

3 √38000000 = 3√32³ × 100³ = 2 × 100 = 200

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

Hence the answer is b.

Question 11. What is the smallest number that can be multiplied by 72 to make it
a perfect cube?

a. 2
b. 4
c. 3
d. 6

Click here for the answer

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.

Question 12. What is the smallest number by which 88 should be divided to get a
perfect cube?

a. 11
b. 7
c. 9
d. 5

Click here for the answer

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.

Question 13. Find the one’s digit of the cube of the number 5022?

a. 2
b. 6
c. 8
d. 4

Click here for the answer

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.

Question 14. How can the cube of 2a be expressed?

a. 4a3
b. 2a2
c. 16a3
d. 8a3

Click here for the answer

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.

Question 15. Which of the following numbers is a perfect cube?

a. 400
b. 2025
c. 15625
d. 9000

Click here for the answer

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.

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