Cube Root of 1000000

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, ∛1000000 is written as 1000000^(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 1000000, then y³ can be 1000000. Since 1000000 is a perfect cube, the cube root of 1000000 is exactly 100.

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 1000000. The common methods we follow to find the cube root are given below:

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

Since 1000000 is a perfect cube, the prime factorization method can be effectively used.

Let's find the cube root of 1000000 using the prime factorization method. First, express 1000000 as a product of its prime factors: 1000000 = 10⁶ = (2 × 5)⁶ = 2⁶ × 5^6

To find the cube root, we take one-third of the powers of each prime factor: ∛1000000 = 2^(6/3) × 5^(6/3) = 2^2 × 5^2 = 4 × 25 = 100 Therefore, the cube root of 1000000 is 100.

• 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. For example: 10 × 10 × 10 = 1000, therefore, 1000 is a perfect cube.

• Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In 1000000^(1/3), ⅓ is the exponent which denotes the cube root.

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

• Rational number: The numbers that can be expressed as a fraction or whole numbers are rational. For example, the cube root of 1000000 is rational because it is a whole number, 100.