Cube Root of 29791

We have learned the definition of the cube root. Now, let’s learn how it is represented using a symbol and exponent. The symbol we use to express the cube root is the radical sign (∛), and the exponent we use is ⅓.

In exponential form, ∛29791 is written as 29791^(1/3). The cube root is just the opposite operation of finding the cube of a number. For example: Assume ‘y’ as the cube root of 29791, then y³ can be 29791. Since the cube root of 29791 is an exact value, it is 31.

Finding the cube root of a number is to identify the number that must be multiplied three times resulting in the target number. Now, we will go through the different ways to find the cube root of 29791. The common methods we follow to find the cube root are given below:

• Prime factorization method
• Approximation method
• Subtraction method
• Halley’s method

To find the cube root of a perfect cube, we often follow the prime factorization method. Since 29791 is a perfect cube, we use the prime factorization method.

Let's find the cube root of 29791 using the prime factorization method.

First, perform the prime factorization of 29791:

29791 = 31 × 31 × 31

Since all the prime factors are grouped into triples, the cube root of 29791 is 31.

Cube root: The number that is multiplied three times by itself to get the given number is the cube root of that number.

Perfect cube: A number is a perfect cube when it is the product of multiplying a number three times by itself. For example: 31 × 31 × 31 = 29791, therefore, 29791 is a perfect cube.

Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In a^(1/3), 1/3 is the exponent which denotes the cube root of a.

Radical sign: The symbol that is used to represent a root is expressed as (∛).

Rational number: A number that can be expressed as a ratio of integers. The cube root of 29791 is rational because it equals 31.