Cube Root of 5832

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, ∛5832 is written as 38321/3. The cube root is just the opposite operation of finding the cube of a number. For example: Assume ‘y’ as the cube root of 5832, then y³ can be 5832. The cube root of 5832 is an exact value, which is 18.

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 5832. The common methods we follow to find the cube root are given below:

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

Since 5832 is a perfect cube, we can effectively use the prime factorization method to find its cube root.

Let's find the cube root of 5832 using the prime factorization method.

First, we factorize 5832: 5832 = 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3

Grouping the factors in triples: = 2³ × 3⁶

Taking the cube root of each group: ∛(2³ × 3⁶) = 2 × 3² = 18

Thus, the cube root of 5832 is 18.

• 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 that is the product of multiplying a number three times by itself. For example, 18³ = 5832, so 5832 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, expressed as (∛).
   
• Irrational number: Numbers that cannot be put in fractional forms. The cube root of non-perfect cubes is often irrational, but the cube root of 5832 is rational.