Cube Root of 512000

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, ∛512000 is written as 512000^(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 512000, then y³ can be 512000. The cube root of 512000 is an exact value, which is 80.

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 512000. The common methods we follow to find the cube root are given below:

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

For 512000, we can use the prime factorization method because it is a perfect cube.

Let's find the cube root of 512000 using the prime factorization method.

The prime factorization of 512000 is: 512000 = 2⁹ × 5³

Now, to find the cube root, we take the cube root of each factor: ∛(2⁹ × 5³) = 2^(9/3) × 5^(3/3) = 2³ × 5¹ = 8 × 5 = 40

The cube root of 512000 is 80.

• 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 512000 is rational because it is 80.