100 LearnersLast updated on June 2nd, 2025
Cube of 650
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
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.
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.
- By Multiplication Method
- Using a Formula
- 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. 650³ = 650 × 650 × 650
Step 2: You get 274,625,000 as the answer. Hence, the cube of 650 is 274,625,000.
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.
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.
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.
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
Incorrect Multiplication
Kids might multiply the numbers only twice. That is, 650 × 650 and not 650 × 650 × 650. Always remember that 650³ = 650 × 650 × 650.
Solved Examples on Cube of 650
Problem 1
What is the cube and cube root of 650?
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.
Problem 2
If the side length of the cube is 650 cm, what is the volume?
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.
Problem 3
How much larger is 650³ than 600³?
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.
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?
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.
Problem 5
Estimate the cube of 649.9 using the cube of 650.
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.
FAQs on Cube of 650
1.What are the perfect cubes up to 650?
2.How do you calculate 650³?
3.What is the meaning of 650³?
4.What is the cube root of 650?
5.Is 650 a perfect cube?
6.How does learning Algebra help students in Philippines make better decisions in daily life?
7.How can cultural or local activities in Philippines support learning Algebra topics such as Cube of 650?
8.How do technology and digital tools in Philippines support learning Algebra and Cube of 650?
9.Does learning Algebra support future career opportunities for students in Philippines?
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.
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Jaskaran Singh Saluja
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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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