Cube Root of 33698267

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, ∛33698267 is written as 33698267^(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 33698267, then y³ can be 33698267. Since the cube root of 33698267 is not an exact whole number, we can write it as approximately 320.996.

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 33698267. 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 large number like 33698267, we often use the approximation method. Since 33698267 is not a perfect cube, we use Halley’s method for better precision.

Let's find the cube root of 33698267 using Halley’s method.

The formula is: ∛a ≅ x((x³ + 2a) / (2x³ + a))

where: a = the number for which the cube root is being calculated

x = the nearest perfect cube

Substituting, a = 33698267;

x = 320

∛a ≅ 320((320³ + 2 × 33698267) / (2 × 320³ + 33698267))

∛33698267 ≅ 320.996

The cube root of 33698267 is approximately 320.996.

• Cube root: The number that is multiplied three times by itself to get the given number is the cube root of that number.
   
• Approximation method: A method used to find a close estimate of the cube root when the exact value is not a whole 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: 2 × 2 × 2 = 8, therefore, 8 is a perfect cube.
   
• Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In x^(1/3), ⅓ is the exponent which denotes the cube root of x.
   
• Radical sign: The symbol that is used to represent a root, which is expressed as (∛).