Cube Root of 157464

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, ∛157464 is written as 157464^(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 157464, then y³ can be 157464. Since the cube root of 157464 is an exact value, we can write it as 54.

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 157464. The common methods we follow to find the cube root are given below:

• Prime factorization method
• Exact cube method

Since 157464 is a perfect cube, we can use the prime factorization method.

Let's find the cube root of 157464 using the prime factorization method:

First, we perform the prime factorization of 157464:

157464 = 2³ × 3³ × 7³ × 13

Grouping the prime factors in triples, we get:

157464 = (2 × 3 × 7)³ × 13

The cube root is the product of the bases in each group:

∛157464 = 2 × 3 × 7 = 42

However, since 157464 is a perfect cube, this step reveals the calculation error.

Recalculating, the correct prime factorization, we find:

157464 = 54³

Thus, ∛157464 = 54.

• 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: 54 × 54 × 54 = 157464.
   
• Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In 157464^(1/3), ⅓ is the exponent which denotes the cube root of 157464.
   
• Radical sign: The symbol that is used to represent a root is expressed as (∛).
   
• Rational number: A number that can be expressed as a fraction of two integers, such as 54, which is the cube root of 157464.