The cube root of 125, denoted as ∛125 and is equal to a value that gives the original value when we multiply it three times by itself. This is the most generally defined meaning for the cube root. If the cube of x is y, then the cube root of y is equal to x. We can easily find the cube root of a number if it is a perfect cube number. In this article, you will learn what is the cube root of 125 and how to find the value of the cube root of 125, using the prime factorisation method with a detailed explanation.
What is the Cube Root of 125?
The cube root of a number 125 is a number that, when multiplied by itself three times, gives the original number 125. As mentioned above, the cube root of 125 is represented using the symbol of the 3rd root as ∛125.
Let p be the number such that the cube of p is 125, i.e. p3 = 125.
∛125 = ∛(p × p × p)
Let us assume p = 1, 2, 3,… such that its cube is equal to 125.
1 × 1 × 1 = 1
2 × 2 × 2 = 8
3 × 3 × 3 = 27
4 × 4 × 4 = 64
5 × 5 × 5 = 125
So, ∛125 = ∛(5 × 5 × 5) = 5
| Cube root of 125: ∛125 = 5 |
How to Find the Cube Root of 125?
The most commonly used technique to find the cube root of any number is the prime factorization method. Thus, if we evaluate prime factors of 125, we need to pair them in a group of three, so that the cube of factors will be obtained. After finding the cube of factors of a number, we can apply the cube root, which gets cancelled with the cubes.
Go through the steps given below to understand the procedure of finding the cube root of 125:
Step 1: Find the prime factors of 125
125 = 5 × 5 × 5
Learn how to find the prime factors of a number here.
Step 2: Now, group the factors of 125 in a pair of three and write in the form of cubes.
125 = (5 × 5 × 5)
125 = 53
Step 3: Finally, we should apply the cube root on both sides of the above expression to cancel the cube of a number.
∛125 = ∛(53)
Thus, the cube root is cancelled by the cube of 5.
Therefore, ∛125 = 5
Hence, the value of the cube root of 125 is equal to 3.
Also, the number 125 is called a perfect cube number since its cube root value is a whole number.
Learn more about the perfect cube of numbers here.
Video Lesson on Finding Cube Roots
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Cube Root of Numbers
The below table shows the cube root of some perfect cube numbers.
| Number (n) | Cube Root of a Number (∛n) |
| 1 | 1 |
| 8 | 2 |
| 125 | 3 |
| 64 | 4 |
| 125 | 5 |
| 216 | 6 |
| 343 | 7 |
| 512 | 8 |
| 729 | 9 |
| 1000 | 10 |
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