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Last updated on June 5th, 2025

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Cube of 747

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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 747.

Cube of 747 for Australian Students
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Cube of 747

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 multiplied by itself three times results in a negative number.

 

The cube of 747 can be written as 747³, which is the exponential form. Or it can also be written in arithmetic form as, 747 × 747 × 747.

 

cube of 747

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How to Calculate the Value of Cube of 747

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 more easily 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. 747³ = 747 × 747 × 747

 

Step 2: You get 416,224,523 as the answer. Hence, the cube of 747 is 416,224,523.

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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 747 into two parts, as 700 and 47. Let a = 700 and b = 47, so a + b = 747

 

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

 

Step 3: Calculate each term a³ = 700³ 3a²b = 3 × 700² × 47 3ab² = 3 × 700 × 47² b³ = 47³

 

Step 4: Add all the terms together:

 

(a + b)³ = a³ + 3a²b + 3ab² + b³

 

(700 + 47)³ = 700³ + 3 × 700² × 47 + 3 × 700 × 47² + 47³

 

747³ = 343,000,000 + 69,300,000 + 46,197 + 103,823

 

747³ = 416,224,523

 

Step 5: Hence, the cube of 747 is 416,224,523.

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Using a Calculator

To find the cube of 747 using a calculator, input the number 747 and use the cube function (if available) or multiply 747 × 747 × 747. This operation calculates the value of 747³, resulting in 416,224,523. 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 4 and then 7

 

Step 3: If the calculator has a cube function, press it to calculate 747³.

 

Step 4: If there is no cube function on the calculator, simply multiply 747 three times manually.

 

Step 5: The calculator will display 416,224,523.

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Tips and Tricks for the Cube of 747

  • 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 747

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, 747 × 747 and not 747 × 747 × 747. Always remember that 747³ = 747 × 747 × 747.

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Solved Examples on Cube of 747

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Problem 1

What is the cube and cube root of 747?

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The cube of 747 is 416,224,523 and the cube root of 747 is approximately 8.994.

Explanation

First, let’s find the cube of 747.

 

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 747³ = 416,224,523

 

Next, we must find the cube root of 747 We know that the cube root of a number ‘x’ is such that ³√x = y Where ‘x’ is the given number, and y is the cube root value of the number

 

So, we get ³√747 ≈ 8.994

 

Hence, the cube of 747 is 416,224,523 and the cube root of 747 is approximately 8.994.

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Problem 2

If the side length of a cube is 747 cm, what is the volume?

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The volume is 416,224,523 cm³.

Explanation

Use the volume formula for a cube V = Side³.

 

Substitute 747 for the side length: V = 747³ = 416,224,523 cm³.

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Problem 3

How much larger is 747³ than 700³?

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747³ – 700³ = 73,224,523.

Explanation

First, find the cube of 747³, which is 416,224,523

 

Next, find the cube of 700³, which is 343,000,000

 

Now, find the difference between them using the subtraction method. 416,224,523 – 343,000,000 = 73,224,523

 

Therefore, 747³ is 73,224,523 larger than 700³.

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Problem 4

If a cube with a side length of 747 cm is compared to a cube with a side length of 47 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 747 cm is 416,224,523 cm³

Explanation

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

 

Cubing 747 means multiplying 747 by itself three times: 747 × 747 = 558,009, and then 558,009 × 747 = 416,224,523.

 

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

 

Therefore, the volume of the cube is 416,224,523 cm³.

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Problem 5

Estimate the cube of 746.9 using the cube of 747.

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The cube of 746.9 is approximately 416,224,523.

Explanation

First, identify the cube of 747, The cube of 747 is 747³ = 416,224,523.

 

Since 746.9 is only a tiny bit less than 747, the cube of 746.9 will be almost the same as the cube of 747.

 

The cube of 746.9 is approximately 416,224,523 because the difference between 746.9 and 747 is very small.

 

So, we can approximate the value as 416,224,523.

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FAQs on Cube of 747

1.What are the perfect cubes up to 747?

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2.How do you calculate 747³?

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3.What is the meaning of 747³?

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4.What is the cube root of 747?

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5.Is 747 a perfect cube?

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

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7.How can cultural or local activities in Australia support learning Algebra topics such as Cube of 747?

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8.How do technology and digital tools in Australia support learning Algebra and Cube of 747?

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

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Important Glossaries for Cube of 747

  • 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, which equals 8.

 

  • Volume: A measure of the amount of space an object occupies, calculated for cubes as the side length raised to the power of three.

 

  • Perfect Cube: A number that can be expressed as an integer raised to the power of three.
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About BrightChamps in Australia

At BrightChamps, algebra is much more than digits—it opens doors to unlimited possibilities! We are committed to helping kids all across Australia master important math skills, including today’s focus on the Cube of 747, with a special spotlight on cubes—in a fun, engaging, and easy-to-understand way. Whether your child is calculating the speed of a roller coaster at Luna Park Sydney, keeping score at a local cricket match, or managing their allowance for the latest gadgets, mastering algebra builds their confidence for daily life. Our interactive lessons make math learning simple and enjoyable. Because children in Australia learn in different ways, we adapt our approach to suit each child’s style. From Sydney’s vibrant streets to the beautiful beaches of the Gold Coast, BrightChamps brings algebra to life, making it exciting and relatable all over Australia. Let’s make cubes a fun 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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