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105 LearnersLast updated on September 18, 2025
Cube of 1421
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 1421.
Cube of 1421
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 1421 can be written as 1421³, which is the exponential form. Or it can also be written in arithmetic form as 1421 × 1421 × 1421.
How to Calculate the Value of Cube of 1421
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 methods will help in cubing numbers faster and easier without confusion when evaluating 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 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. 1421³ = 1421 × 1421 × 1421
Step 2: You get 2,870,034,061 as the answer. Hence, the cube of 1421 is 2,870,034,061.
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 1421 into two parts, such as a and b. Let a = 1400 and b = 21, so a + b = 1421
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term
a³ = 1400³
3a²b = 3 × 1400² × 21
3ab² = 3 × 1400 × 21²
b³ = 21³
Step 4: Add all the terms together:
(a + b)³ = a³ + 3a²b + 3ab² + b³
(1400 + 21)³ = 1400³ + 3 × 1400² × 21 + 3 × 1400 × 21² + 21³
1421³ = 2,744,000,000 + 1,234,800 + 617,400 + 9,261
1421³ = 2,870,034,061
Step 5: Hence, the cube of 1421 is 2,870,034,061.
Using a Calculator
To find the cube of 1421 using a calculator, input the number 1421 and use the cube function (if available) or multiply 1421 × 1421 × 1421. This operation calculates the value of 1421³, resulting in 2,870,034,061. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 1 followed by 4, 2, 1
Step 3: If the calculator has a cube function, press it to calculate 1421³.
Step 4: If there is no cube function on the calculator, simply multiply 1421 three times manually.
Step 5: The calculator will display 2,870,034,061.
Tips and Tricks for the Cube of 1421
- 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 1421
There are some typical errors that might occur during the process of cubing a number. Let us take a look at five of the major mistakes that might be made:
Mistake 1
Incorrect Multiplication
Mistakes can occur when multiplying the numbers only twice, such as 1421 × 1421 and not 1421 × 1421 × 1421. Always remember that 1421³ = 1421 × 1421 × 1421.
Mistake 2
Misunderstanding the Cube Formula
There is a possibility of confusion between the formulas for square numbers and cube numbers. The square number formula is (a + b)² and the cube number formula is (a + b)³. Always review the formula to understand the difference between squaring and cubing.
Mistake 3
Calculator Misuse
Pressing the wrong buttons, such as using the square (x²) function instead of the cube (x³) function or skipping steps in manual multiplication. Always double-check your inputs on the calculator, and if it lacks a cube function, perform the multiplication in steps.
Mistake 4
Misplacing Zeros
Misplacing zeros during manual multiplication can lead to incorrect results like 2,870,034,061 being written as 2,870,034,61. Double-check your answers to avoid this.
Mistake 5
Ignoring the Binomial Formula
Errors might occur when splitting 1421 into 1400 + 21 but not applying the correct binomial expansion. Carefully calculate each term step-by-step during the application of the formula.
Solved Examples on Cube of 1421
Problem 1
What is the cube and cube root of 1421?
The cube of 1421 is 2,870,034,061 and the cube root of 1421 is approximately 11.157.
Explanation
First, let’s find the cube of 1421.
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 1421³ = 2,870,034,061
Next, we must find the cube root of 1421. We know that 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 ∛1421 ≈ 11.157
Hence, the cube of 1421 is 2,870,034,061 and the cube root of 1421 is approximately 11.157.
Problem 2
If the side length of the cube is 1421 cm, what is the volume?
The volume is 2,870,034,061 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 1421 for the side length: V = 1421³ = 2,870,034,061 cm³.
Problem 3
How much larger is 1421³ than 1400³?
1421³ – 1400³ = 126,034,061.
Explanation
First, find the cube of 1421³, which is 2,870,034,061.
Next, find the cube of 1400³, which is 2,744,000,000.
Now, find the difference between them using the subtraction method. 2,870,034,061 – 2,744,000,000 = 126,034,061
Therefore, 1421³ is 126,034,061 larger than 1400³.
Problem 4
If a cube with a side length of 1421 cm is compared to a cube with a side length of 21 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 1421 cm is 2,870,034,061 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 1421 means multiplying 1421 by itself three times: 1421 × 1421 = 2,019,841, and then 2,019,841 × 1421 = 2,870,034,061.
The unit of volume is cubic centimeters (cm³) because we are calculating the space inside the cube.
Therefore, the volume of the cube is 2,870,034,061 cm³.
Problem 5
Estimate the cube of 1419 using the cube of 1421.
The cube of 1419 is approximately 2,870,034,061.
Explanation
First, identify the cube of 1421, The cube of 1421 is 1421³ = 2,870,034,061.
Since 1419 is only slightly less than 1421, the cube of 1419 will be almost the same as the cube of 1421.
The cube of 1419 is approximately 2,870,034,061 because the difference between 1419 and 1421 is very small.
So, we can approximate the value as 2,870,034,061.
FAQs on Cube of 1421
1.What are the perfect cubes up to 1421?
2.How do you calculate 1421³?
3.What is the meaning of 1421³?
4.What is the cube root of 1421?
5.Is 1421 a perfect cube?
Important Glossaries for Cube of 1421
- 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.
- Multiplication Method: A mathematical process used to find the product of numbers by combining them through repeated addition.
- Perfect Cube: A number that is the cube of an integer. For example, 27 is a perfect cube because it is 3 × 3 × 3.
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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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: He loves to play the quiz with kids through algebra to make kids love it.
