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Last updated on June 5th, 2025

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Cube of 723

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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 723.

Cube of 723 for US Students
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Cube of 723

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 multiplying a negative number by itself three times results in a negative number.

 

The cube of 723 can be written as 723³, which is the exponential form. Or it can also be written in arithmetic form as, 723 × 723 × 723.

 

cube of 723

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How to Calculate the Value of Cube of 723

In order to check whether a number is a cube number or not, we can use the following three methods, such as 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.

 

  1. By Multiplication Method
  2. Using a Formula
  3. Using a Calculator
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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. 723³ = 723 × 723 × 723

 

Step 2: You get 377,933,067 as the answer. Hence, the cube of 723 is 377,933,067.

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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 723 into two parts, as 700 and 23. Let a = 700 and b = 23, so a + b = 723

 

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

 

Step 3: Calculate each term

 

a³ = 700³

 

3a²b = 3 × 700² × 23

 

3ab² = 3 × 700 × 23²

 

b³ = 23³

 

Step 4: Add all the terms together:

 

(a + b)³ = a³ + 3a²b + 3ab² + b³

 

(700 + 23)³ = 700³ + 3 × 700² × 23 + 3 × 700 × 23² + 23³

 

723³ = 343,000,000 + 33,810,000 + 11,109,300 + 12,167

 

723³ = 377,933,067

 

Step 5: Hence, the cube of 723 is 377,933,067.

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Using a Calculator

To find the cube of 723 using a calculator, input the number 723 and use the cube function (if available) or multiply 723 × 723 × 723. This operation calculates the value of 723³, resulting in 377,933,067. It’s a quick way to determine the cube without manual computation.

 

Step 1: Ensure the calculator is functioning properly.

 

Step 2: Enter 7 followed by 2 and 3.

 

Step 3: If the calculator has a cube function, press it to calculate 723³.

 

Step 4: If there is no cube function on the calculator, simply multiply 723 three times manually.

 

Step 5: The calculator will display 377,933,067.

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Tips and Tricks for the Cube of 723

  • 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.
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Common Mistakes to Avoid When Calculating the Cube of 723

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:

Mistake 1

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Incorrect Multiplication

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Kids might multiply the numbers only twice. That is, 723 × 723 and not 723 × 723 × 723. Always remember that 723³ = 723 × 723 × 723.

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Solved Examples on Cube of 723

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Problem 1

What is the cube and cube root of 723?

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The cube of 723 is 377,933,067 and the cube root of 723 is approximately 8.985.

Explanation

First, let’s find the cube of 723.

 

We know that cube of a number, such that x³ = y Where x is the given number, and y is the cubed value of that number

 

So, we get 723³ = 377,933,067

 

Next, we must find the cube root of 723 We know that the cube root of a number ‘x’, such that ∛x = y Where ‘x’ is the given number, and y is the cube root value of the number

 

So, we get ∛723 ≈ 8.985

 

Hence, the cube of 723 is 377,933,067 and the cube root of 723 is approximately 8.985.

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Problem 2

If the side length of the cube is 723 cm, what is the volume?

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The volume is 377,933,067 cm³.

Explanation

Use the volume formula for a cube V = Side³.

 

Substitute 723 for the side length: V = 723³ = 377,933,067 cm³.

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Problem 3

How much larger is 723³ than 500³?

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723³ – 500³ = 314,933,067.

Explanation

First, find the cube of 723, that is 377,933,067

 

Next, find the cube of 500, which is 125,000,000

 

Now, find the difference between them using the subtraction method. 377,933,067 – 125,000,000 = 314,933,067

 

Therefore, 723³ is 314,933,067 larger than 500³.

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Problem 4

If a cube with a side length of 723 cm is compared to a cube with a side length of 100 cm, how much larger is the volume of the larger cube?

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The volume of the cube with a side length of 723 cm is 377,933,067 cm³.

Explanation

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

 

Cubing 723 means multiplying 723 by itself three times: 723 × 723 = 522,729, and then 522,729 × 723 = 377,933,067.

 

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

 

Therefore, the volume of the cube is 377,933,067 cm³.

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Problem 5

Estimate the cube of 722 using the cube of 723.

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The cube of 722 is approximately 377,933,067.

Explanation

First, identify the cube of 723, The cube of 723 is 723³ = 377,933,067.

 

Since 722 is only a tiny bit less than 723, the cube of 722 will be almost the same as the cube of 723.

 

The cube of 722 is approximately 377,933,067 because the difference between 722 and 723 is very small.

 

So, we can approximate the value as 377,933,067.

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FAQs on Cube of 723

1.What are the perfect cubes up to 723?

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2.How do you calculate 723³?

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3.What is the meaning of 723³?

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4.What is the cube root of 723?

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5.Is 723 a perfect cube?

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6.How does learning Algebra help students in United States make better decisions in daily life?

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7.How can cultural or local activities in United States support learning Algebra topics such as Cube of 723?

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8.How do technology and digital tools in United States support learning Algebra and Cube of 723?

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9.Does learning Algebra support future career opportunities for students in United States?

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Important Glossaries for Cube of 723

  • 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. It is denoted as ∛x.

 

  • Volume of a Cube: The volume of a cube is the space within a cube, calculated as the side length raised to the power of three (Side³).
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About BrightChamps in United States

At BrightChamps, we believe algebra is more than just symbols—it’s a gateway to endless possibilities! Our goal is to support kids all across the United States in mastering essential math concepts, like today’s focus on the Cube of 723, especially the fascinating world of cubes—in a way that’s engaging, clear, and enjoyable. Whether your child is calculating how quickly a roller coaster zooms through Disney World, tracking scores at a Little League baseball game, or budgeting their allowance for new gadgets, understanding algebra builds the confidence they need for daily life. Our hands-on lessons make math both accessible and fun. Since children in the USA learn in diverse ways, we customize our teaching to match each student’s learning style. From the energetic streets of New York City to the sunny beaches of California, BrightChamps brings algebra to life, making it exciting and relevant across America. Let’s make cubes an exciting part of every child’s math journey!
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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.

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Fun Fact

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

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