BrightChamps Logo
Login
Creative Math Ideas Image
Live Math Learners Count Icon100 Learners

Last updated on June 2nd, 2025

Math Whiteboard Illustration

Cube of 650

Professor Greenline Explaining Math Concepts

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 cubes of 650.

Cube of 650 for Canadian Students
Professor Greenline from BrightChamps

Cube of 650

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 650 can be written as 650³, which is the exponential form. Or it can also be written in arithmetic form as, 650 × 650 × 650.

 

cube of 650

Professor Greenline from BrightChamps

How to Calculate the Value of Cube of 650

In order to check whether a number is a cube number or not, we can use the following three methods: the 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
Professor Greenline from BrightChamps

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. 650³ = 650 × 650 × 650

 

Step 2: You get 274,625,000 as the answer. Hence, the cube of 650 is 274,625,000.

Professor Greenline from BrightChamps

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 650 into two parts, as a and b. Let a = 600 and b = 50, so a + b = 650

 

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

 

Step 3: Calculate each term

 

a³ = 600³

 

3a²b = 3 × 600² × 50

 

3ab² = 3 × 600 × 50²

 

b³ = 50³

 

Step 4: Add all the terms together:

 

(a + b)³ = a³ + 3a²b + 3ab² + b³

 

(600 + 50)³ = 600³ + 3 × 600² × 50 + 3 × 600 × 50² + 50³

 

650³ = 216,000,000 + 54,000,000 + 4,500,000 + 125,000

 

650³ = 274,625,000

 

Step 5: Hence, the cube of 650 is 274,625,000.

Professor Greenline from BrightChamps

Using a Calculator

To find the cube of 650 using a calculator, input the number 650 and use the cube function (if available) or multiply 650 × 650 × 650. This operation calculates the value of 650³, resulting in 274,625,000. It’s a quick way to determine the cube without manual computation.

 

Step 1: Ensure the calculator is functioning properly.

 

Step 2: Press 6 followed by 5 and 0

 

Step 3: If the calculator has a cube function, press it to calculate 650³.

 

Step 4: If there is no cube function on the calculator, simply multiply 650 three times manually.

 

Step 5: The calculator will display 274,625,000.

Professor Greenline from BrightChamps

Tips and Tricks for the Cube of 650

  • 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.
Max Pointing Out Common Math Mistakes

Common Mistakes to Avoid When Calculating the Cube of 650

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

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Incorrect Multiplication

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

Kids might multiply the numbers only twice. That is, 650 × 650 and not 650 × 650 × 650. Always remember that 650³ = 650 × 650 × 650.

Max from BrightChamps Saying "Hey"

Solved Examples on Cube of 650

Ray, the Character from BrightChamps Explaining Math Concepts
Max, the Girl Character from BrightChamps

Problem 1

What is the cube and cube root of 650?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

The cube of 650 is 274,625,000 and the cube root of 650 is approximately 8.672.

Explanation

First, let’s find the cube of 650. We know that the 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 650³ = 274,625,000

 

Next, we must find the cube root of 650 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 ∛650 ≈ 8.672

 

Hence the cube of 650 is 274,625,000 and the cube root of 650 is approximately 8.672.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 2

If the side length of the cube is 650 cm, what is the volume?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

The volume is 274,625,000 cm³.

Explanation

Use the volume formula for a cube V = Side³.

 

Substitute 650 for the side length: V = 650³ = 274,625,000 cm³.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 3

How much larger is 650³ than 600³?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

650³ – 600³ = 58,625,000.

Explanation

First, find the cube of 650³, which is 274,625,000

 

Next, find the cube of 600³, which is 216,000,000

 

Now, find the difference between them using the subtraction method.

 

274,625,000 – 216,000,000 = 58,625,000

 

Therefore, 650³ is 58,625,000 larger than 600³.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 4

If a cube with a side length of 650 cm is compared to a cube with a side length of 100 cm, how much larger is the volume of the larger cube?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

The volume of the cube with a side length of 650 cm is 274,625,000 cm³, which is much larger than the volume of the cube with a side length of 100 cm.

Explanation

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

 

Cubing 650 means multiplying 650 by itself three times: 650 × 650 = 422,500, and then 422,500 × 650 = 274,625,000.

 

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

 

Therefore, the volume of the cube is 274,625,000 cm³.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 5

Estimate the cube of 649.9 using the cube of 650.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

The cube of 649.9 is approximately 274,625,000.

Explanation

First, identify the cube of 650, The cube of 650 is 650³ = 274,625,000.

 

Since 649.9 is only a tiny bit less than 650, the cube of 649.9 will be almost the same as the cube of 650.

 

The cube of 649.9 is approximately 274,625,000 because the difference between 649.9 and 650 is very small.

 

So, we can approximate the value as 274,625,000.

Max from BrightChamps Praising Clear Math Explanations
Ray Thinking Deeply About Math Problems

FAQs on Cube of 650

1.What are the perfect cubes up to 650?

Math FAQ Answers Dropdown Arrow

2.How do you calculate 650³?

Math FAQ Answers Dropdown Arrow

3.What is the meaning of 650³?

Math FAQ Answers Dropdown Arrow

4.What is the cube root of 650?

Math FAQ Answers Dropdown Arrow

5.Is 650 a perfect cube?

Math FAQ Answers Dropdown Arrow

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

Math FAQ Answers Dropdown Arrow

7.How can cultural or local activities in Canada support learning Algebra topics such as Cube of 650?

Math FAQ Answers Dropdown Arrow

8.How do technology and digital tools in Canada support learning Algebra and Cube of 650?

Math FAQ Answers Dropdown Arrow

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

Math FAQ Answers Dropdown Arrow
Professor Greenline from BrightChamps

Important Glossaries for Cube of 650

  • 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 to 8.

 

  • Multiplication Method: A process in mathematics used to find the product of numbers by combining them through repeated addition.

 

  • Perfect Cube: A number that can be expressed as the product of an integer multiplied by itself twice more.
Professor Greenline from BrightChamps

About BrightChamps in Canada

At BrightChamps, we understand algebra goes beyond digits—it opens doors to limitless possibilities! We aim to guide kids all across Canada to grasp key math skills, such as today’s focus on the Cube of 650, with a special emphasis on exploring cubes—in a fun, engaging, and easy-to-understand manner. Whether your child is measuring the speed of a roller coaster at Canada’s Wonderland, tracking hockey game scores, or budgeting their allowance for the latest gadgets, mastering algebra builds their everyday confidence. Our engaging lessons make learning both enjoyable and simple. Since Canadian children learn in various ways, we tailor our teaching to suit each learner’s style. From Toronto’s vibrant city life to the breathtaking views of British Columbia, BrightChamps makes algebra come alive, making it meaningful and exciting across Canada. Let’s make cubes a thrilling part of every child’s math story!
Math Teacher Background Image
Math Teacher Image

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.

Math Teacher Fun Facts Image
Max, the Girl Character from BrightChamps

Fun Fact

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

INDONESIA - Axa Tower 45th floor, JL prof. Dr Satrio Kav. 18, Kel. Karet Kuningan, Kec. Setiabudi, Kota Adm. Jakarta Selatan, Prov. DKI Jakarta
INDIA - H.No. 8-2-699/1, SyNo. 346, Rd No. 12, Banjara Hills, Hyderabad, Telangana - 500034
SINGAPORE - 60 Paya Lebar Road #05-16, Paya Lebar Square, Singapore (409051)
USA - 251, Little Falls Drive, Wilmington, Delaware 19808
VIETNAM (Office 1) - Hung Vuong Building, 670 Ba Thang Hai, ward 14, district 10, Ho Chi Minh City
VIETNAM (Office 2) - 143 Nguyễn Thị Thập, Khu đô thị Him Lam, Quận 7, Thành phố Hồ Chí Minh 700000, Vietnam
Dubai - BrightChamps, 8W building 5th Floor, DAFZ, Dubai, United Arab Emirates
UK - Ground floor, Redwood House, Brotherswood Court, Almondsbury Business Park, Bristol, BS32 4QW, United Kingdom