Cube of 75
2026-02-28 09:08 Diff
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Last updated on August 5, 2025

When a number is multiplied by itself thrice, the resultant number is called the cube of a number. Cubing is used when comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of 75.

Cube of 75

A cube number is a value obtained by raising a number to the power of 3, or by multiplying the number by itself three times.

When you cube a positive number, the result is always positive.

When you cube a negative number, the result is always negative.

This is because a negative number by itself three times results in a negative number.

The cube of 75 can be written as 75³, which is the exponential form.

Or it can also be written in arithmetic form as, 75 × 75 × 75.

How to Calculate the Value of Cube of 75

In order to check whether a number is a cube number or not, we can use the following three methods: multiplication method, a factor formula (a³), or by using a calculator. These three methods will help kids to cube the numbers faster and easier without feeling confused or stuck while evaluating the answers.

  • By Multiplication Method
     
  • Using a Formula (a3)
     
  • Using a Calculator

By Multiplication Method

The multiplication method is a process in mathematics used to find the product of two numbers or quantities by combining them through repeated addition. It is a fundamental operation that forms the basis for more complex mathematical concepts.

Step 1: Write down the cube of the given number. 75³ = 75 × 75 × 75

Step 2: You get 421,875 as the answer.

Hence, the cube of 75 is 421,875.

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Using a Formula (a³)

The formula (a + b)³ is a binomial formula for finding the cube of a number. The formula is expanded as a³ + 3a²b + 3ab² + b³.

Step 1: Split the number 75 into two parts. Let a = 70 and b = 5, so a + b = 75

Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³

Step 3: Calculate each term a³ = 70³ 3a²b = 3 × 70² × 5 3ab² = 3 × 70 × 5² b³ = 5³

Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (70 + 5)³ = 70³ + 3 × 70² × 5 + 3 × 70 × 5² + 5³ 75³ = 343,000 + 73,500 + 5,250 + 125 75³ = 421,875

Step 5: Hence, the cube of 75 is 421,875.

Using a Calculator

To find the cube of 75 using a calculator, input the number 75 and use the cube function (if available) or multiply 75 × 75 × 75. This operation calculates the value of 75³, resulting in 421,875. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Press 7 followed by 5

Step 3: If the calculator has a cube function, press it to calculate 75³.

Step 4: If there is no cube function on the calculator, simply multiply 75 three times manually.

Step 5: The calculator will display 421,875.

Tips and Tricks for the Cube of 75

  • The cube of any even number is always even, while the cube of any odd number is always odd.
     
  • The product of two or more perfect cube numbers is always a perfect cube.
     
  • A perfect cube can always be expressed as the product of three identical groups of equal prime factors.

Common Mistakes to Avoid When Calculating the Cube of 75

There are some typical errors that kids might make during the process of cubing a number. Let us take a look at five of the major mistakes that kids might make:

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Problem 1

What is the cube and cube root of 75?

Okay, lets begin

The cube of 75 is 421,875 and the cube root of 75 is approximately 4.217.

Explanation

First, let’s find the cube of 75.

We know that the cube of a number is such that x³ = y

Where x is the given number, and y is the cubed value of that number

So, we get 75³ = 421,875 Next, we must find the cube root of 75

We know that the cube root of a number ‘x’, is such that ∛x = y

Where ‘x’ is the given number, and y is the cube root value of the number

So, we get ∛75 ≈ 4.217

Hence the cube of 75 is 421,875 and the cube root of 75 is approximately 4.217.

Well explained 👍

Problem 2

If the side length of the cube is 75 cm, what is the volume?

Okay, lets begin

The volume is 421,875 cm³.

Explanation

Use the volume formula for a cube V = Side³.

Substitute 75 for the side length: V = 75³ = 421,875 cm³.

Well explained 👍

Problem 3

How much larger is 75³ than 65³?

Okay, lets begin

75³ – 65³ = 211,875.

Explanation

First, find the cube of 75³, which is 421,875

Next, find the cube of 65³, which is 210,000

Now, find the difference between them using the subtraction method. 421,875 – 210,000 = 211,875

Therefore, the 75³ is 211,875 larger than 65³.

Well explained 👍

Problem 4

If a cube with a side length of 75 cm is compared to a cube with a side length of 15 cm, how much larger is the volume of the larger cube?

Okay, lets begin

The volume of the cube with a side length of 75 cm is 421,875 cm³

Explanation

To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).

Cubing 75 means multiplying 75 by itself three times: 75 × 75 = 5,625, and then 5,625 × 75 = 421,875.

The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.

Therefore, the volume of the cube is 421,875 cm³.

Well explained 👍

Problem 5

Estimate the cube 74.9 using the cube 75.

Okay, lets begin

The cube of 74.9 is approximately 421,875.

Explanation

First, identify the cube of 75,

The cube of 75 is 75³ = 421,875.

Since 74.9 is only a tiny bit less than 75, the cube of 74.9 will be almost the same as the cube of 75.

The cube of 74.9 is approximately 421,875 because the difference between 74.9 and 75 is very small.

So, we can approximate the value as 421,875.

Well explained 👍

FAQs on Cube of 75

1.What are the perfect cubes up to 75?

The perfect cubes up to 75 are 1, 8, 27, and 64.

2.How do you calculate 75³?

To calculate 75³, use the multiplication method, 75 × 75 × 75, which equals 421,875.

3.What is the meaning of 75³?

75³ means 75 multiplied by itself three times, or 75 × 75 × 75.

4.What is the cube root of 75?

5.Is 75 a perfect cube?

No, 75 is not a perfect cube because no integer multiplied by itself three times equals 75.

Important Glossaries for Cube of 75

  • Binomial Formula: It is an algebraic expression used to expand the powers of a number, written as (a + b)ⁿ, where ‘n’ is a positive integer raised to the base. The formula is used to find the square and cube of a number.
  • Cube of a Number: Multiplying a number by itself three times is called the cube of a number.
  • Exponential Form: It is a way of expressing numbers using a base and an exponent (or power), where the exponent value indicates how many times the base is multiplied by itself. For example, 2³ represents 2 × 2 × 2 equals 8.
  • Cube Root: The cube root of a number is a value that, when multiplied by itself three times, gives the original number.
  • Volume of a Cube: Calculated by cubing the side length of the cube, represented as Side³.

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Jaskaran Singh Saluja

About the Author

Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.