Cube Root of 1157625

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, ∛1157625 is written as 1157625^(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 1157625, then y³ = 1157625. Since the cube root of 1157625 is an exact value, it is 105.

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 1157625. The common methods we follow to find the cube root are given below:

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

Since 1157625 is a perfect cube, we can use the prime factorization method to find its cube root.

Let's find the cube root of 1157625 using the prime factorization method.

First, we find the prime factors of 1157625: 1157625 = 3 × 3 × 3 × 5 × 5 × 5 × 7 × 7 × 7

Pair the prime factors in triples: (3 × 3 × 3) × (5 × 5 × 5) × (7 × 7 × 7)

The cube root is: ∛1157625 = 3 × 5 × 7 = 105

• 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: 105 × 105 × 105 = 1157625, therefore, 1157625 is a perfect cube.

• Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In 1157625^(1/3), ⅓ is the exponent which denotes the cube root of 1157625.

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

• Rational number: A number that can be expressed as a ratio of two integers, where the denominator is not zero. The cube root of 1157625 is rational because it is exactly 105.