Cube Root of 8000

Cube root of 8000 is equal to 20.

The cube root of 8000 is equal to a value that gives the original value when we multiply it three times by itself and is written as ∛8000. This is the general meaning of 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 8000 and how to find the value of the cube root of 8000 using the prime factorisation method with a detailed explanation.

What is the Cube Root of 8000?

The cube root of a number 8000 is equal to a number that, when multiplied by itself three times, gives the original number 8000. As mentioned above, the cube root of 8000 is represented using the symbol of the 3rd root such as ∛8000.

Let a be the number such that the cube of a is 8000, i.e. a³ = 8000.

∛8000 = ∛(a × a × a)

Let us take a = 1, 2, 3,… such that its cube is equal to 8000.

1 × 1 × 1 = 1

2 × 2 × 2 = 8

3 × 3 × 3 = 27

4 × 4 × 4 = 64

5 × 5 × 5 = 125

….

10 × 10 × 10 = 1000

….

20 × 20 × 20 = 8000

So, ∛8000 = ∛(20 × 20 × 20) = 20

How to Find the Cube Root of 8000?

The technique which is generally used to find the cube root of any number is the prime factorization method. Thus, if we find prime factors of 8000, we have to pair the prime factors 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.

The below steps are used to understand the method of finding the cube root of 8000:

Step 1: First, write the prime factors of 8000

8000 = 2⁶ × 5³ = 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5 × 5

Learn how to find the prime factors of a number here.

Step 2: Let us group the factors of 8000 in a pair of three and write in the form of cubes.

8000 = (2 × 2 × 2) × (2 × 2 × 2) × (5 × 5 × 5)

8000 = 2³ × 2³ × 5³

Step 3: Take the cube root on both sides so that the cube will be cancelled in the RHS.

∛8000 = ∛(2³ × 2³ × 5³) = ∛(2 × 2 × 5)³

Thus, the cube root is cancelled by the cube of ( 2 × 2 × 5).

Therefore, ∛8000 = 2 × 2 × 5 = 20

Hence, the cube root value of 8000 is equal to 20.

However, the number 8000 is called a perfect cube number since its cube root value is a whole number.

Learn more about the perfect cube of numbers here.

Alternative Method:

We can also find the cube root value of 8000 by splitting the number as the product of 8 and 1000. As we know, the cube root of 8 is 2, and the cube root of 1000 is 10. Thus, by multiplying these two values, we can get the cube root of 8000.

∛8000 = ∛(8 × 1000) = ∛8 × ∛1000 = 2 × 10 = 20

Trick to Find the Cube Root of 8000

Observe the number 8000. Here, the last digit is 0, which means the cube root value must end with 0, i.e. the unit digit must be 0. As we know, the square of any number with 0 in its unit’s place contains two zeros in the result and the cube contains three zeros. From this, we can say that the cube root value of 8000 is a two-digit number. Now, coming to the first digit of 8000, 8 is the cube of 2. Thus, by combining these statements, we get the cube root of 8000 as 20.

Video Lesson on Finding Cube Roots

Cube Root of Numbers

The below table shows the cube root of some perfect cube numbers.

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