Cube Root of 250047

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, ∛250047 is written as 250047^(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 250047, then y³ can be 250047. Since 250047 is a perfect cube, the cube root of 250047 is 63.

Finding the cube root of a number is identifying 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 250047. The common methods we follow to find the cube root are given below:

•  Prime factorization method
•  Estimation method
• Halley's method

Since 250047 is a perfect cube, we can use the prime factorization method to find its exact cube root.

Let's find the cube root of 250047 using prime factorization.

First, break down 250047 into its prime factors:

250047 = 3 × 3 × 3 × 7 × 7 × 7 × 13 × 13 × 13

Now, group the prime factors in triples to find the cube root: (3 × 7 × 13) × (3 × 7 × 13) × (3 × 7 × 13)

Thus, ∛250047 = 3 × 7 × 13 = 273.

• 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 results in a whole number. For example, 3 × 3 × 3 = 27.

• 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, expressed as (∛).

• Rational number: Numbers that can be expressed as a fraction of two integers. For example, the cube root of 250047 is rational because it is 63.