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102 LearnersLast updated on August 5, 2025
Cube of 1416
When a number is multiplied by itself thrice, the resultant number is called the cube of a number. Cubing is used when comparing the sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of 1416.
Cube of 1416
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 1416 can be written as 1416³, which is the exponential form. Or it can also be written in arithmetic form as 1416 × 1416 × 1416.
How to Calculate the Value of Cube of 1416
In order to check whether a number is a cube number or not, we can use the following three methods: multiplication method, a formula (a³), or by using a calculator. These three methods will help in cubing 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 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. 1416³ = 1416 × 1416 × 1416
Step 2: Calculate the product. Hence, the cube of 1416 is 2,836,060,416.
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 1416 into two parts. Let a = 1400 and b = 16, so a + b = 1416
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 1400³ 3a²b = 3 × 1400² × 16 3ab² = 3 × 1400 × 16² b³ = 16³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (1400 + 16)³ = 1400³ + 3 × 1400² × 16 + 3 × 1400 × 16² + 16³ 1416³ = 2,744,000,000 + 940,800 + 537,600 + 4,096 1416³ = 2,836,060,416
Step 5: Hence, the cube of 1416 is 2,836,060,416.
Using a Calculator
To find the cube of 1416 using a calculator, input the number 1416 and use the cube function (if available) or multiply 1416 × 1416 × 1416. This operation calculates the value of 1416³, resulting in 2,836,060,416. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Input 1416.
Step 3: If the calculator has a cube function, press it to calculate 1416³.
Step 4: If there is no cube function on the calculator, simply multiply 1416 three times manually.
Step 5: The calculator will display 2,836,060,416.
Tips and Tricks for the Cube of 1416
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 1416
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:
Mistake 1
Incorrect Multiplication
One might multiply the numbers only twice. That is, 1416 × 1416 and not 1416 × 1416 × 1416. Always remember that 1416³ = 1416 × 1416 × 1416.
Mistake 2
Misunderstanding the Cube Formula
There is a possibility of confusion 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
One 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. Always double-check your answers for accuracy.
Mistake 5
Ignoring the Binomial Formula
One might attempt to split the number into parts, but not apply the correct binomial expansion. Carefully calculate each term step-by-step during the application of the formula.
Solved Examples on Cube of 1416
Problem 1
What is the cube and cube root of 1416?
The cube of 1416 is 2,836,060,416 and the cube root of 1416 is approximately 11.153.
Explanation
First, let’s find the cube of 1416. 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 1416³ = 2,836,060,416.
Next, we must find the cube root of 1416. 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 ∛1416 ≈ 11.153. Hence the cube of 1416 is 2,836,060,416 and the cube root of 1416 is approximately 11.153.
Problem 2
If the side length of the cube is 1416 cm, what is the volume?
The volume is 2,836,060,416 cm³.
Explanation
Use the volume formula for a cube V = Side³. Substitute 1416 for the side length: V = 1416³ = 2,836,060,416 cm³.
Problem 3
How much larger is 1416³ than 1000³?
1416³ – 1000³ = 1,836,060,416.
Explanation
First find the cube of 1416³, which is 2,836,060,416. Next, find the cube of 1000³, which is 1,000,000,000. Now, find the difference between them using the subtraction method.
2,836,060,416 – 1,000,000,000 = 1,836,060,416. Therefore, 1416³ is 1,836,060,416 larger than 1000³.
Problem 4
If a cube with a side length of 1416 cm is compared to a cube with a side length of 500 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 1416 cm is 2,836,060,416 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object). Cubing 1416 means multiplying 1416 by itself three times: 1416 × 1416 = 2,003,856, then 2,003,856 × 1416 = 2,836,060,416. The unit of volume is cubic centimeters (cm³) because we are calculating the space inside the cube. Therefore, the volume of the cube is 2,836,060,416 cm³.
Problem 5
Estimate the cube of 1415 using the cube of 1416.
The cube of 1415 is approximately 2,836,060,416.
Explanation
First, identify the cube of 1416. The cube of 1416 is 1416³ = 2,836,060,416. Since 1415 is only slightly less than 1416, the cube of 1415 will be almost the same as the cube of 1416.
The cube of 1415 is approximately 2,836,060,416 because the difference between 1415 and 1416 is very small. So, we can approximate the value as 2,836,060,416.
FAQs on Cube of 1416
1.What are the perfect cubes up to 1416?
2.How do you calculate 1416³?
3.What is the meaning of 1416³?
4.What is the cube root of 1416?
5.Is 1416 a perfect cube?
Important Glossaries for Cube of 1416
- Binomial Formula: An algebraic expression used to expand the powers of a sum, written as (a + b)ʳ, where ‘ʳ’ 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: 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, equaling 8.
- Perfect Cube: A number that is the cube of an integer. For example, 8 is a perfect cube because it equals 2³.
- Cube Root: The value that, when cubed, gives the original number. For example, the cube root of 27 is 3, since 3³ = 27.
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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.
