Cube Root of 8615125

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, ∛8615125 is written as 8615125^(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 8615125, then y³ can be 8615125. Since 8615125 is a perfect cube, its cube root is exactly 205.

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 8615125. The common methods we follow to find the cube root are given below:

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

To find the cube root of a perfect cube like 8615125, we can use the prime factorization method for an exact result.

Let's find the cube root of 8615125 using the prime factorization method:

1. Break down 8615125 into its prime factors: \(8615125 = 5^3 \times 7^3 \times 11^3\).

2. Since each factor is raised to the power of 3, the cube root can be directly obtained by taking one of each factor: - (∛(5^3) = 5) - (∛(7^3) = 7) - (∛(11^3) = 11)

3. Multiply these results: (5 times 7 times 11 = 385).

The cube root of 8615125 is 205.

• 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: \(5 \times 5 \times 5 = 125\), therefore, 125 is a perfect cube.
   
• Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In (8615125^{1/3}), ⅓ is the exponent which denotes the cube root of 8615125.
   
• Radical sign: The symbol that is used to represent a root is expressed as (∛).
   
• Rational number: A number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. The cube root of 8615125 is 205, which is a rational number because it can be expressed as a fraction (205/1).