Cube Root of 27

The cube root of 27, denoted as ∛27 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 a number is a perfect cube, we can easily find the cube root of a number. In this article, you will learn what is the cube root of 27 and how to find the value of the cube root of 27, using the prime factorisation method with a complete explanation.

What is the Cube Root of 27?

The cube root of a number 27 is a number that, when multiplied by itself three times, results in the original number 27. The cube root of 27 is symbolically represented as ∛27.

∛27 = ∛(Number × Number × Number)

∛27 = ∛(3 × 3 × 3)

∛27 = 3

How to Find the Cube Root of 27?

Generally, we apply the prime factorization method to find the prime factors of the given number. Therefore, once we evaluate prime factors of 27, we need to pair them in a group of three, giving the cube of factors. After finding the cube of factors of a number, we can apply the cube root, which gets cancelled with the cubes.

Let us understand it in a step-by-step procedure.

Step 1: Find the prime factors of 27

27 = 3 × 3 × 3

Step 2: Clearly, 27 is a perfect cube. Therefore, group the factors of 27 in a pair of three and write in the form of cubes.

27 = 3 × 3 × 3

27 = 3³

Step 3: Now, we should apply the cube root on both sides of the above expression to take out the term in cubes.

∛27 = ∛(3³)

So, the cube root is cancelled by the cube of 3.

Therefore, ∛27 = 3

Hence, the value of the cube root of 27 is equal to 3.

Also, we can say that 27 is a perfect cube number since its cube root value is a whole number.

Know about the perfect cube of numbers here.

Cube Root of Numbers

Let us have a look at the cube root of some perfect cube numbers given in the below table.

Solved Examples

Example 1:

Find the side of a cube whose volume is given by 27 cm³.

Solution:

Let a be the side of a cube.

Given,

Volume = 27 cm³

i.e. a³ = 27

a = ∛27 = 3

Therefore, the measure of a side of the cube is 3 cm.

Example 2:

Simplify: 5 – ∛27 + 3 × 15

Solution:

5 – ∛27 + 3 × 15 = 5 – 3 + 3 × 15 {since the cube root of 27 is 3}

= 5 – 3 + 45

= 50 – 3

= 47

Therefore, 5 – ∛27 + 3 × 15 = 47

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