Cube Root of 3.375

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, ∛3.375 is written as 3.375^(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 3.375, then y^3 can be 3.375. Since the cube root of 3.375 is an exact value, we can write it as 1.5.

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 3.375. 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 non-perfect cube, we often follow Halley’s method, but since 3.375 is a perfect cube, we can use the prime factorization method.

Let's find the cube root of 3.375 using the prime factorization method.

First, express 3.375 as a product of its prime factors: 3.375 = 3 × 3 × 3 × 5/2 × 5/2 × 5/2

Group the factors into three identical sets: (3 × 5/2) × (3 × 5/2) × (3 × 5/2)

So, the cube root of 3.375 is 3 × 5/2 = 1.5.

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

Children often try to calculate an exact whole number for the cube root of numbers like 3.375, which is a perfect cube. For example, they might assume 3.375 doesn’t have a whole number cube root. To avoid this error, memorize that 3.375 is a perfect cube with a cube root of 1.5.

Most of us might forget the fact that the cube root can also be written in exponent form.

For example: Forgetting that the cube root of 3.375 is 3.375^(1/3). To avoid this error, always learn the forms in which we can express the cube root of a number. plain_heading7 Confusing cube root with division plain_body7 Assuming the cube root of 3.375 is to divide 3.375 by 3.

For example, mistakenly assume 3.375 ÷ 3 = 1.5 is the cube root. To avoid this, remember that the cube root of 3.375 is the number you multiply by itself three times to get 3.375.

• 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, 1.5 × 1.5 × 1.5 = 3.375, therefore, 3.375 is a perfect cube.

• Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In 3.375^(1/3), ⅓ is the exponent which denotes the cube root of 3.375.

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

• Rational number: A number that can be expressed as a fraction or ratio, such as 1.5, which is the cube root of 3.375.