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105 LearnersLast updated on August 5, 2025
Cube of 1414
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 1414.
Cube of 1414
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 1414 can be written as 1414³, which is the exponential form.
Or it can also be written in arithmetic form as 1414 × 1414 × 1414.
How to Calculate the Value of Cube of 1414
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 (\(a^3\)), 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.
1414³ = 1414 × 1414 × 1414
Step 2: You get 2,828,804,344 as the answer.
Hence, the cube of 1414 is 2,828,804,344.
Using a Formula (\(a^3\))
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 1414 into two parts.
Let a = 1400 and b = 14, so a + b = 1414
Step 2: Now, apply the formula:
(a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term:
a³ = 1400³
3a²b = 3 × 1400² × 14
3ab² = 3 × 1400 × 14²
b³ = 14³
Step 4: Add all the terms together:
(1400 + 14)³ = 1400³ + 3 × 1400² × 14 + 3 × 1400 × 14² + 14³
Step 5: Hence, the cube of 1414 is 2,828,804,344.
Using a Calculator
To find the cube of 1414 using a calculator, input the number 1414 and use the cube function (if available) or multiply 1414 × 1414 × 1414. This operation calculates the value of 1414³, resulting in 2,828,804,344. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Input 1414.
Step 3: If the calculator has a cube function, press it to calculate 1414³.
Step 4: If there is no cube function on the calculator, simply multiply 1414 three times manually.
Step 5: The calculator will display 2,828,804,344.
Tips and Tricks for the Cube of 1414
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 1414
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, 1414 × 1414 and not 1414 × 1414 × 1414. Always remember that 1414³ = 1414 × 1414 × 1414.
Mistake 2
Misunderstanding the Cube Formula
There is a possibility that kids might be confused between the formulas of 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 for the difference between squaring and cubing.
Mistake 3
Calculator Misuse
Kids might press the wrong buttons, such as using the square (\(x^2\)) function instead of the cube (\(x^3\)) 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. For this, kids should always double-check their answers.
Mistake 5
Ignoring the Binomial Formula
Kids might attempt to split the 1414 into 1400 + 14, but not apply the correct binomial expansion. In order to avoid this, carefully calculate each term step-by-step during the application of the formula.
Solved Examples on Cube of 1414
Problem 1
What is the cube and cube root of 1414?
The cube of 1414 is 2,828,804,344, and the cube root of 1414 is approximately 11.144.
Explanation
First, let’s find the cube of 1414. 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 1414³ = 2,828,804,344.
Next, we must find the cube root of 1414. 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 ∛1414 ≈ 11.144.
Hence, the cube of 1414 is 2,828,804,344, and the cube root of 1414 is approximately 11.144.
Problem 2
If the side length of the cube is 1414 cm, what is the volume?
The volume is 2,828,804,344 cm\(^3\).
Explanation
Use the volume formula for a cube:
V = Side³
Substitute 1414 for the side length:
V = 1414³ = 2,828,804,344 cm³
Problem 3
How much larger is \(1414^3\) than \(1400^3\)?
1414³ - 1400³ = 2,828,804,344 - 2,740,000,000 = 88,804,344
Explanation
First, find the cube of 1414³, which is 2,828,804,344.
Next, find the cube of 1400³, which is 2,744,000,000.
Now, find the difference between them using the subtraction method:
2,828,804,344 − 2,744,000,000 = 84,804,344.
Therefore, 1414³ is 84,804,344 larger than 1400³.
(Looks like the earlier difference had a small calculation error.)
Problem 4
If a cube with a side length of 1414 cm is compared to a cube with a side length of 14 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 1414 cm is significantly larger at 2,828,804,344 cm3
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 1414 means multiplying 1414 by itself three times:
1414 × 1414 = 1,999,396
1,999,396 × 1414 = 2,828,804,344
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 2,828,804,344 cm³.
Problem 5
Estimate the cube 1413.9 using the cube 1414.
The cube of 1413.9 is approximately 2,828,804,344.
Explanation
First, identify the cube of 1414, which is 1414³ = 2,828,804,344.
Since 1413.9 is only a tiny bit less than 1414, the cube of 1413.9 will be almost the same as the cube of 1414.
The cube of 1413.9 is approximately 2,828,804,344 because the difference between 1413.9 and 1414 is very small.
So, we can approximate the value as 2,828,804,344.
FAQs on Cube of 1414
1.What are the perfect cubes up to 1414?
2.How do you calculate \(1414^3\)?
3.What is the meaning of \(1414^3\)?
4.What is the cube root of 1414?
5.Is 1414 a perfect cube?
Important Glossaries for Cube of 1414
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Binomial Formula: An algebraic expression used to expand the powers of a number, written as (a + b)ⁿ, where ‘n’ is a positive integer. The formula is used to find the square and cube of a number.
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Cube of a Number: Multiplying a number by itself three times.
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Exponential Form: A way of expressing numbers using a base and an exponent. For example, 2³ means 2 × 2 × 2 = 8.
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Perfect Cube: A number that can be expressed as the cube of an integer.
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Cube Root: A value that, when multiplied by itself three times, gives the original number. For example, the cube root of 8 is 2.
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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.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
