Cube Root of 3375

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, ∛3375 is written as 3375^(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 3375, then y³ can be 3375. Since the cube root of 3375 is an exact value, we can write it as 15.

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 3375. 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, we often follow the prime factorization method. Since 3375 is a perfect cube, we use the prime factorization method.

Let's find the cube root of 3375 using the prime factorization method.

Step 1: Perform prime factorization of 3375: 3375 = 3 × 3 × 3 × 5 × 5 × 5

Step 2: Group the prime factors into triples: (3 × 3 × 3) and (5 × 5 × 5)

Step 3: Take one factor from each group: 3 and 5 Multiply the results: 3 × 5 = 15

The cube root of 3375 is 15.

• 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: 15 × 15 × 15 = 3375, therefore, 3375 is a perfect cube.

• Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In 3375^(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: Numbers that can be expressed as a fraction or a whole number. The cube root of 3375 is rational because it is 15, a whole number.