Cube Root of 2401

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, ∛2401 is written as 2401^1/3. The cube root is just the opposite operation of finding the cube of a number. For example: Assume ‘y’ as the cube root of 2401, then y³ can be 2401. Since the cube root of 2401 is an exact value, we can write it as 13.

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 2401. 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 number like 2401, we can use the prime factorization method or other straightforward methods.

Let's find the cube root of 2401 using the prime factorization method.

First, we find the prime factors of 2401: 2401 = 7 × 7 × 7 × 7

Group the factors into triples of the same number: (7 × 7) × (7 × 7) = (7^2) × (7^2)

Therefore, the cube root of 2401 is 7² = 49.

Finding the perfect cube of a number without any errors can be a difficult task for the students. This happens for many reasons. Here are a few mistakes the students commonly make and the ways to avoid them:

• 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: 7 × 7 × 7 = 343, therefore, 343 is a perfect cube.

• Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In 2401^1/3, ⅓ is the exponent which denotes the cube root.

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

• Rational number: The numbers that can be expressed as a fraction are rational. For example, the cube root of 2401 is rational because it equals 13, which can be expressed as 13/1.