Cube of 723
2026-02-28 23:29 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 723.

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.

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

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.

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.

Tips and Tricks for the Cube of 723

  • 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 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:

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Problem 1

What is the cube and cube root of 723?

Okay, lets begin

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.

Well explained 👍

Problem 2

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

Okay, lets begin

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.

Well explained 👍

Problem 3

How much larger is 723³ than 500³?

Okay, lets begin

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.

Well explained 👍

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?

Okay, lets begin

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.

Well explained 👍

Problem 5

Estimate the cube of 722 using the cube of 723.

Okay, lets begin

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.

Well explained 👍

FAQs on Cube of 723

1.What are the perfect cubes up to 723?

The perfect cubes up to 723 are 1, 8, 27, 64, 125, 216, 343, 512, and 729.

2.How do you calculate 723³?

To calculate 723³, use the multiplication method, 723 × 723 × 723, which equals 377,933,067.

3.What is the meaning of 723³?

723³ means 723 multiplied by itself three times, or 723 × 723 × 723.

4.What is the cube root of 723?

5.Is 723 a perfect cube?

No, 723 is not a perfect cube because no integer multiplied by itself three times equals 723.

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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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.