Cube Root of 27

Cube Root of 27 denoted as ∛27 or (27)^1/3, is equal to 3 which means that if you multiply 3 by itself three times (3 × 3 × 3), you will get 27. Cube roots are the inverse operation of cubing a number, and they are often used in various mathematical and scientific calculations.

In this article, we will answer the question i.e. “What is the Cube Root of 27?” and other than this we will also learn various methods for the same.

Cube Root Definition

Cube Root of a number is a mathematical operation that determines a value which, when multiplied by itself three times (cubed), equals the original number.

Cube Root is denoted by the symbol ∛ and is the inverse operation of cubing a number. In other words, if x³ = a, then the cube root of ‘a’ is ∛a = x.

Value of Cube Root of 27

Cube Root of 27 is 3 and it can be represented by ∛27 or (27)^1/3. Also,

∛27 = ∛3 × 3 × 3 = ∛(3)³ = (3³)^1/3 = (3)^{3 × 1/3} = 3

Cube Root of 27 Calculator

How to Calculate the Value of the Cube Root of 27?

To calculate the Cube root of 27 we can use two method first is prime factorization method as 27 is a perfect cube number. Let’s discuss this method in detail as follows:

Prime Factorization Method

The prime factorization method is the simpler method to calculate the cube root of any number. The cube root of 27 is calculated by finding the factors of it. The prime factor of 27 is 3 multiplied by three times.

Prime Factorization of 27

Prime Factorization of 27 = 3 × 3 × 3

For any number, if there are three same factors in prime factorization, it is the cube root of given number. Thus, cube root of 27 is 3 by prime factorization method.

Is the Cube Root of 27 Irrational?

Cube root of 27 is 3 which is a rational number because it can be expressed in the form of (P/Q) i.e. 3/1 , and the value of denominators is not equal to 0 i.e. 0 ≭ 1.

Hence, we can say that the cube root of 27 is not an irrational number.

Solved Examples on Cube root of 27

Example 1: What is the length of side of a cube box it its volume is 27 cube unit?

Solution:

Volume of a cube = (side)³

Length of side of cube = (volume)^1/3

⇒ Length of side = (27)^1/3

⇒ Length of side = (3)^{3 × 1/3}

⇒ Length of side = 3 unit

The length of the side of the cube is 3 unit.

Example 2: If Ayush got total of 27 rupees in three days from his father. The amount of money his father gave him are equal. What is the amount of money his father gave him everyday?

Solution:

He got total of 27 rupees.

His father gave him equal amount daily in three days

So, the amount he will get in one day = 27/3 = 3.

The answer is 3 rupees.

Example 3: What is the radius of hemisphere if its volume is 18π cm³ ?

Solution:

Volume of hemisphere = 2/3πr³ , where r is radius

⇒ 2/3πr³ = 18π cm³

⇒ r³ = (18π × 3)/ 2π

⇒ r = 3cm

The radius of hemisphere is 3cm.

Cube Root of 27: FAQs

How do you Find the Cube Root?

To find the cube root of a number, you can use the ∛ symbol or a calculator. Simply take the number and raise it to the power of 1/3. For example, ∛27 = 3.

What is Cube Root of 2718?

Cube root of 2718 is approximately equal to 14.190.

What is Negative Cube Root of 27?

Negative cube root of 27 is approximately -3.

What is Cube of 3?

The cube of 3 is 27.

Is 27 a Perfect Cube?

27 is a perfect cube , as 3 is the cube root of 27.

Is Cube Root of 27 a Rational Number or Irrational Number?

The cube root of 27 is 3 and it is rational number. 3 is a rational number because it can be expressed in the form of (P/Q) i.e. 3/1, and the value of denominators is not equal to 0 i.e. 0 ≭ 1.