Cube root questions are given here to help the students enhance their skills in performing various mathematical operations on numbers. As we know, cubes and cube root of numbers are the important concepts of Class 8 Mathematics. So, practising the cube root questions given below will help you to score good marks in the corresponding examination. In this article, you will get the questions on cube root with detailed solutions.
Cube Root Definition
The cube root of a number is the value that gives the original numbers when multiplied thrice. Suppose y is the cube root of x, ∛x = y, such that x = y3 = y . y . y. Here, ∛ denotes the cube root of a number. If the cube root of a number is a whole number, that number is called the perfect cube.
Learn: Cube root
The below table shows the cube roots of perfect cube numbers.
| Cube root | Cube |
| ∛1 = 1 | 13 = 1 |
| ∛8 = 2 | 23 = 8 |
| ∛27 = 3 | 33 = 27 |
| ∛64 = 4 | 43 = 64 |
| ∛125 = 5 | 53 = 125 |
| ∛216 = 6 | 63 = 216 |
| ∛343 = 7 | 73 = 343 |
| ∛512 = 8 | 83 = 512 |
| ∛729 = 9 | 93 = 729 |
| ∛1000 = 10 | 103 = 1000 |
How to Find the Cube Root of Numbers?
We can find the cube root of a given number in different ways such as prime factorization. Also, for cube numbers, we can find the cube root through estimation.
Cube Root Questions and Answers
1. Find the cube root of 74088 through estimation.
Solution:
Given number: 74088
Step 1: Form groups of three starting from the rightmost digit of 74088.
i.e. (74) (088)
In this case, one group, i.e., 088, has three digits, whereas the other group, i.e. 74, has only two digits.
Step 2: Consider the group with three digits, i.e. 088.
The digit 8 is at its one’s place. We take the one’s place of the required cube root as 2, since the cube of a number with unit place 2 will result in the number with units place 8.
Step 3: Take the other group, i.e., 74. which lies between 64 and 125. The cube of 4 is 64, and the cube of 5 is 125.
43 < 74 < 53
and 4 < 5
The one’s place of 4 is 4 itself. So, take 4 as ten’s place of the cube root of 74088.
Thus, ∛74088 = 42.
2. Find the value of the cube root of 5832 by prime factorization.
Solution:
Given number: 5832
Given number: 46656
Let us write the prime factorization of 46656.
46656 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3
Form the group of three prime factors that are equal.
46656 = (2 x 2 x 2) x (2 x 2 x 2) x (3 x 3 x 3) x (3 x 3 x 3)
46656 = 23 x 23 x 33 x 33
Take the cube root on both sides.
∛46656 = ∛(23 x 23 x 33 x 33) = 2 x 2 x 3 x 3 = 36
Therefore, the cube root of 46656 is 36.
3. How do you find the cube root of 91125 through estimation?
Solution:
Given number: 91125
Step 1: Form groups of three starting from the rightmost digit of 91125.
i.e. (91) (125)
In this case, one group, i.e., 125, has three digits, whereas the other group, i.e. 91, has only two digits.
Step 2: Consider the group with three digits, i.e. 125.
The digit 5 is at its one’s place. We take the one’s place of the required cube root as 5, since the cube of a number with unit place 5 will result in the number with units place 5.
Step 3: Take the other group, i.e.,91, which lies between 64 and 125. The cube of 4 is 64, and the cube of 5 is 125.
43 < 91 < 53
and 4 < 5
The one’s place of 4 is 4 itself. So, take 4 as ten’s place of the cube root of 91125.
Thus, ∛91125 = 45.
4. Find the cube root of 0.001331.
Solution:
Given number: 0.001331
This can be written as:
0.001331 = 1331 × 10-6
= 1331/106
= (11 × 11 × 11)/(102 × 102 × 102)
= (11)3/ (102)3
i.e. 0.001331 = (11)3/(102)3
Take cube root on both sides,
∛0.001331 = ∛[(11)3/(102)3]
= 11/102
= 0.11
Therefore, the cube root of 0.001331 is 0.11.
5. What is the cube root of 8788?
Solution:
Given number: 8788
First, write the prime factorization of 8788.
8788 = 2 x 2 x 13 x 13 x 13
Form the group of three prime factors that are equal.
8788 = 2 x 2 x (13 x 13 x 13)
Take the cube root on both sides.
∛8788 = ∛[2 x 2 x (13 x 13 x 13)]
= 13 ∛(2 x 2)
= 13 ∛4
6. Find the cube root of the perfect cube number 571787.
Solution:
Given number: 571787
Let us find the cube root of 571787 through estimation since it is given that 571787 is a perfect cube number.
Step 1: Form groups of three starting from the rightmost digit of 74088.
i.e. (571) (787)
Here, both the groups contain three digits.
Step 2: Consider the group with three digits from the rightmost, i.e. 787.
The digit 7 is at its one’s place. We take the one’s place of the required cube root as 3, since the cube of a number with unit place 3 will result in the number with units place 7. For example, 33 = 27.
Step 3: Take the other group, i.e., 571. which lies between 512 and 729. The cube of 8 is 512, and the cube of 9 is 729.
83 < 571 < 93
and 8 < 9
So, take 8 as ten’s place of the cube root of 571787.
Thus, ∛571787 = 83.
7. Find the smallest number, which, when multiplied with 3600, will make the product a perfect cube. Further, find the cube root of the product.
Solution:
First, write the prime factorization of 3600.
3600 = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5
= 23 × 32 × 52 × 2
Only one triple is formed here, and three factors remain ungrouped in triples.
Thus, the given number 3600 is not a perfect cube.
To make it a perfect cube, we have to multiply it by (3 × 5 × 22) so that the factors will form triples.
So, 3600 × 3 × 5 × 22 = 3600 × 60 = 216000
Cube root of 216000 = ∛216000
= ∛(23 × 23 × 33 × 53)
= ∛(2 × 2 × 3 × 5)
= 60
∴ The smallest number multiplied by 3600, which will make the product a perfect cube is 60, and the cube root of the product is 60.
8. What is the cube root of 13824?
Solution:
First, write the prime factorization of 13824.
13824 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3
Form the group of three prime factors that are equal.
13824 = (2 x 2 x 2) x (2 x 2 x 2) x (2 x 2 x 2) x 3 x 3 x 3)
13824 = 23 x 23 x 23 x 33
Take the cube root on both sides.
∛13824 = ∛(23 x 23 x 23 x 33)
= 2 x 2 x 2 x 3
= 24
Hence, the value of the cube root of 13824 is 24.
9. Check whether 30 is a cube root of 27000.
Solution:
We know that, if y is the cube root of x, ∛x = y, then x = y3 = y . y . y
So, to check whether 30 is a cube root of 27000, we need to find the cube of 30.
Thus, 303 = 30 x 30 x 30 = 27000
Therefore, 30 is the cube root of 27000.
10. Find the cube root of 64/343.
Solution:
Given fraction: 64/343
Let us write the prime factorization of both numerator and denominator.
64 = 2 x 2 x 2 x 2 x 2 x 2 = (2 x 2 x 2) x (2 x 2 x 2) = 23 x 23
343 = 7 x 7 x 7 = 73
Now,
∛(64/343) = ∛[(23 x 23)/73]
= (2 x 2)/7
= 4/7
Hence, the cube root of 64/343 is 4/7.
Video Lesson on Finding Cube Roots
Practice Questions on Cube Root
- What is the cube root of 17576?
- Find the cube root of 857375 through estimation.
- Find the cube root of 0.000512.
- You are told that 1331 is a perfect cube. Can you guess without factorization what its cube root is? Similarly, guess the cube roots of 4913, 12167, 32768.
- What is the value of the cube root of 10648?
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