100 LearnersLast updated on June 2nd, 2025
Cube of 681
When a number is multiplied by itself thrice, the resultant number is called the cube of a number. Cubing is used while comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about cubes of 681.
Cube of 681
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 by itself three times results in a negative number.
The cube of 681 can be written as 681³, which is the exponential form. Or it can also be written in arithmetic form as, 681 × 681 × 681.
How to Calculate the Value of Cube of 681
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.
- 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. 681³ = 681 × 681 × 681
Step 2: You get 315,622,041 as the answer. Hence, the cube of 681 is 315,622,041.
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 681 into two parts as needed. Let a = 680 and b = 1, so a + b = 681
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term
a³ = 680³
3a²b = 3 × 680² × 1
3ab² = 3 × 680 × 1²
b³ = 1³
Step 4: Add all the terms together:
(a + b)³ = a³ + 3a²b + 3ab² + b³
(680 + 1)³ = 680³ + 3 × 680² × 1 + 3 × 680 × 1² + 1³
681³ = 314,432,000 + 1,387,200 + 2,040 + 1
681³ = 315,622,041
Step 5: Hence, the cube of 681 is 315,622,041.
Using a Calculator
To find the cube of 681 using a calculator, input the number 681 and use the cube function (if available) or multiply 681 × 681 × 681. This operation calculates the value of 681³, resulting in 315,622,041. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 6, 8, followed by 1
Step 3: If the calculator has a cube function, press it to calculate 681³.
Step 4: If there is no cube function on the calculator, simply multiply 681 three times manually.
Step 5: The calculator will display 315,622,041.
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 681
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, 681 × 681 and not 681 × 681 × 681. Always remember that 681³ = 681 × 681 × 681.
Solved Examples on Cube of 681
Problem 1
What is the cube and cube root of 681?
The cube of 681 is 315,622,041 and the cube root of 681 is approximately 8.802.
Explanation
First, let’s find the cube of 681.
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 681³ = 315,622,041
Next, we must find the cube root of 681 We know that the cube root of a number ‘x’, 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√681 ≈ 8.802
Hence the cube of 681 is 315,622,041 and the cube root of 681 is approximately 8.802.
Problem 2
If the side length of the cube is 681 cm, what is the volume?
The volume is 315,622,041 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 681 for the side length: V = 681³ = 315,622,041 cm³.
Problem 3
How much larger is 681³ than 680³?
681³ – 680³ = 1,389,241.
Explanation
First find the cube of 681³, that is 315,622,041
Next, find the cube of 680³, which is 314,432,000
Now, find the difference between them using the subtraction method. 315,622,041 – 314,432,000 = 1,389,241
Therefore, 681³ is 1,389,241 larger than 680³.
Problem 4
If a cube with a side length of 681 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 681 cm is 315,622,041 cm³
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 681 means multiplying 681 by itself three times: 681 × 681 = 463,761, and then 463,761 × 681 = 315,622,041.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 315,622,041 cm³.
Problem 5
Estimate the cube 680.9 using the cube 681.
The cube of 680.9 is approximately 315,622,041.
Explanation
First, identify the cube of 681, The cube of 681 is 681³ = 315,622,041.
Since 680.9 is only a tiny bit less than 681, the cube of 680.9 will be almost the same as the cube of 681.
The cube of 680.9 is approximately 315,622,041 because the difference between 680.9 and 681 is very small.
So, we can approximate the value as 315,622,041.
FAQs on Cube of 681
1.What are the perfect cubes up to 681?
2.How do you calculate 681³?
3.What is the meaning of 681³?
4.What is the cube root of 681?
5.Is 681 a perfect cube?
6.How does learning Algebra help students in United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Cube of 681?
8.How do technology and digital tools in United States support learning Algebra and Cube of 681?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for Cube of 681
- 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.
- Perfect Cube: A number that can be expressed as the cube of an integer.
- Volume of a Cube: The amount of space occupied by a cube, calculated as the side length raised to the power of three.
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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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