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104 LearnersLast updated on August 5, 2025
Cube of 1419
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 1419.
Cube of 1419
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 1419 can be written as 1419³, which is the exponential form. Or it can also be written in arithmetic form as 1419 × 1419 × 1419.
How to Calculate the Value of Cube of 1419
In order to check whether a number is a cube number or not, we can use the following three methods, such as the multiplication method, a factor formula (a³), or by using a calculator. These three methods will help kids to cube numbers faster and easier without feeling confused or stuck while evaluating the answers.
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By Multiplication Method
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Using a Formula
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Using a Calculator
By Multiplication Method
The multiplication method is a process in mathematics used to find the product of numbers 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.
1419³ = 1419 × 1419 × 1419
Step 2: You get 2,858,618,659 as the answer.
Hence, the cube of 1419 is 2,858,618,659.
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 1419 into two parts.
Let a = 1400 and b = 19, so a + b = 1419.
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³.
Step 3: Calculate each term:
a³ = 1400³
3a²b = 3 × 1400² × 19
3ab² = 3 × 1400 × 19²
b³ = 19³
Step 4: Add all the terms together:
(1400 + 19)³ = 1400³ + 3 × 1400² × 19 + 3 × 1400 × 19² + 19³
1419³ = 2,744,000,000 + 111,720,000 + 1,008,600 + 6,859
1419³ = 2,858,618,659
Step 5: Hence, the cube of 1419 is 2,858,618,659.
Using a Calculator
To find the cube of 1419 using a calculator, input the number 1419 and use the cube function (if available) or multiply 1419 × 1419 × 1419. This operation calculates the value of 1419³, resulting in 2,858,618,659. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Input the number 1419.
Step 3: If the calculator has a cube function, press it to calculate 1419³.
Step 4: If there is no cube function on the calculator, simply multiply 1419 three times manually.
Step 5: The calculator will display 2,858,618,659.
Tips and Tricks for the Cube of 1419
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 1419
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, 1419 × 1419 and not 1419 × 1419 × 1419. Always remember that 1419³ = 1419 × 1419 × 1419.
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 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, leads to incorrect results like 2,858,618,65 instead of 2,858,618,659. For this, kids should always double-check their answers.
Mistake 5
Ignoring the Binomial Formula
Kids might attempt to split the 1419 into 1400 + 19, 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 1419
Problem 1
What is the cube and cube root of 1419?
The cube of 1419 is 2,858,618,659 and the cube root of 1419 is approximately 11.162.
Explanation
First, let’s find the cube of 1419. 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 1419³ = 2,858,618,659.
Next, we must find the cube root of 1419. 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 ∛1419 ≈ 11.162.
Hence the cube of 1419 is 2,858,618,659 and the cube root of 1419 is approximately 11.162.
Problem 2
If the side length of a cube is 1419 cm, what is the volume?
The volume is 2,858,618,659 cm³.
Explanation
Use the volume formula for a cube: V = Side³
Substitute 1419 for the side length:
V = 1419³ = 2,858,618,659 cm³
Problem 3
How much larger is \(1419^3\) than \(1000^3\)?
1419³ - 1000³ = 2,858,618,659 - 1,000,000,000 = 1,858,618,659
Explanation
First find the cube of 1419³, which is 2,858,618,659.
Next, find the cube of 1000³, which is 1,000,000,000.
Now, find the difference between them using the subtraction method:
2,858,618,659 − 1,000,000,000 = 1,858,618,659.
Therefore, 1419³ is 1,858,618,659 larger than 1000³.
Problem 4
If a cube with a side length of 1419 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 1419 cm is 2,858,618,659 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 1419 means multiplying 1419 by itself three times:
1419 × 1419 = 2,014,761, and then 2,014,761 × 1419 = 2,858,618,659.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 2,858,618,659 cm³.
Problem 5
Estimate the cube of 1418.5 using the cube of 1419.
The cube of 1418.5 is approximately 2,858,618,659.
Explanation
First, identify the cube of 1419.
The cube of 1419 is 1419³ = 2,858,618,659.
Since 1418.5 is only a tiny bit less than 1419, the cube of 1418.5 will be almost the same as the cube of 1419.
The cube of 1418.5 is approximately 2,858,618,659 because the difference between 1418.5 and 1419 is very small.
So, we can approximate the value as 2,858,618,659.
FAQs on Cube of 1419
1.What are the perfect cubes up to 1419?
2.How do you calculate \(1419^3\)?
3.What is the meaning of \(1419^3\)?
4.What is the cube root of 1419?
5.Is 1419 a perfect cube?
Important Glossaries for Cube of 1419
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Binomial Formula: An expression used to expand powers of sums, written as (a + b)ⁿ, useful for finding squares and cubes of numbers.
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Cube of a Number: The result of multiplying a number by itself three times.
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Exponential Form: A way to represent repeated multiplication using a base and exponent; e.g., 2³ = 2 × 2 × 2 = 8.
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Perfect Cube: A number that is the cube of an integer (e.g., 27 is a perfect cube because 3³ = 27).
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Volume of a Cube: The space a cube occupies, calculated as side³.
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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.
