Cube Root of 531441

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, ∛531441 is written as 531441^(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 531441, then y³ can be 531441. The cube root of 531441 is an exact value, which is 81.

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 531441. The common methods we follow to find the cube root are given below: 

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

Since 531441 is a perfect cube, we use the prime factorization method to find its cube root.

Let's find the cube root of 531441 using the prime factorization method.

First, we find the prime factors of 531441. 531441 = 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 = 3^12

Since we want the cube root, we divide the power by 3: 3^(12/3) = 3^4 = 81

Thus, the cube root of 531441 is 81.

• 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, 81 is the cube root of 531441.
   
• Exponent: The exponent form of a number denotes the number of times a number can be multiplied by itself. In 531441^(1/3), ⅓ is the exponent which denotes the cube root of 531441.
   
• Radical sign: The symbol used to represent a root is expressed as (∛).
   
• Rational number: Numbers that can be expressed as a fraction or whole number. The cube root of 531441 is rational because it is 81.