Cube Root of 1331000

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, ∛1331000 is written as 1331000^(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 1331000, then y³ can be 1331000. The cube root of 1331000 is an exact value, which is 110.

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 1331000. The common methods we follow to find the cube root are given below:

- Prime factorization method

- Estimation method

- Halley’s method

To find the cube root of a perfect cube number, we can follow the prime factorization method. Since 1331000 is a perfect cube, prime factorization is an efficient method here.

Let's find the cube root of 1331000 using the prime factorization method.

First, we perform prime factorization of 1331000: 1331000 = 2 × 2 × 2 × 5 × 5 × 5 × 11 × 11 × 11

Grouping the prime factors in triples: (2 × 2 × 2) × (5 × 5 × 5) × (11 × 11 × 11)

Taking the cube root of each group gives us: ∛1331000 = 2 × 5 × 11 = 110

Therefore, the cube root of 1331000 is 110.

• 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, 110 × 110 × 110 = 1331000, therefore, 1331000 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), ⅓ is the exponent which denotes the cube root of a.

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

• Rational number: A number that can be expressed as a fraction or an exact value. For example, the cube root of 1331000 is rational because it is exactly 110.