Cube Root of 681472

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, ∛681472 is written as 681472^(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 681472, then y³ can be 681472. Since the cube root of 681472 is an exact value, we can write it as exactly 88.

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 681472. The common methods we follow to find the cube root are given below:

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

Since 681472 is a perfect cube, we can use the prime factorization method.

Let's find the cube root of 681472 using the prime factorization method.

First, we find the prime factors of 681472:

681472 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 11 × 11 × 11

Grouping the factors in triples, we have: (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × (11 × 11 × 11)

Taking one factor from each group, we get: ∛681472 = 2 × 2 × 2 × 11 = 88

The cube root of 681472 is exactly 88.

• 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: 4 × 4 × 4 = 64, therefore, 64 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 ratio of two integers. The cube root of 681472 is rational because it is exactly 88.