Cube Root of 6859

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, ∛6859 is written as 6859^(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 6859, then y³ can be 6859. Since the cube root of 6859 is an exact value, it is 19.

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 6859. The common methods we follow to find the cube root are given below:

• Prime factorization method
• Direct calculation method
• Estimation method

To find the cube root of a perfect cube, we can use the prime factorization method or direct calculation method since 6859 is a perfect cube.

Let's find the cube root of 6859 using the prime factorization method. First, we find the prime factors of 6859: 6859 = 19 × 19 × 19 Since we have three identical factors of 19, the cube root of 6859 is 19.

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. A perfect cube always results in a whole number. For example: 19 × 19 × 19 = 6859, therefore, 6859 is a perfect cube.

Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In 6859^(1/3), ⅓ is the exponent which denotes the cube root of 6859.

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

Rational number: Numbers that can be expressed as a fraction or whole number. The cube root of 6859 is rational because it is exactly 19.