101 LearnersLast updated on May 26th, 2025
Cube of 429
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 the cube of 429.
Cube of 429
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 429 can be written as 429³, which is the exponential form. Or it can also be written in arithmetic form as, 429 × 429 × 429.
How to Calculate the Value of Cube of 429
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 (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. 429³ = 429 × 429 × 429 Step 2: You get 78,998,589 as the answer. Hence, the cube of 429 is 78,998,589.
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 429 into two parts, as 400 and 29. Let a = 400 and b = 29, so a + b = 429 Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³ Step 3: Calculate each term a³ = 400³ 3a²b = 3 × 400² × 29 3ab² = 3 × 400 × 29² b³ = 29³ Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (400 + 29)³ = 400³ + 3 × 400² × 29 + 3 × 400 × 29² + 29³ 429³ = 64,000,000 + 13,920,000 + 1,008,600 + 24,389 429³ = 78,998,589 Step 5: Hence, the cube of 429 is 78,998,589.
Using a Calculator
To find the cube of 429 using a calculator, input the number 429 and use the cube function (if available) or multiply 429 × 429 × 429. This operation calculates the value of 429³, resulting in 78,998,589. It’s a quick way to determine the cube without manual computation. Step 1: Ensure the calculator is functioning properly. Step 2: Press 4 followed by 2 and 9 Step 3: If the calculator has a cube function, press it to calculate 429³. Step 4: If there is no cube function on the calculator, simply multiply 429 three times manually. Step 5: The calculator will display 78,998,589.
Tips and Tricks for the Cube of 429
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 429
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, 429 × 429 and not 429 × 429 × 429. Always remember that 429³ = 429 × 429 × 429.
Solved Examples on Cube of 429
Problem 1
What is the cube and cube root of 429?
The cube of 429 is 78,998,589 and the cube root of 429 is approximately 7.519.
Explanation
First, let’s find the cube of 429. 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 429³ = 78,998,589 Next, we must find the cube root of 429 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 ∛429 ≈ 7.519 Hence, the cube of 429 is 78,998,589 and the cube root of 429 is approximately 7.519.
Problem 2
If the side length of the cube is 429 cm, what is the volume?
The volume is 78,998,589 cm³.
Explanation
Use the volume formula for a cube V = Side³. Substitute 429 for the side length: V = 429³ = 78,998,589 cm³.
Problem 3
How much larger is 429³ than 400³?
429³ – 400³ = 14,998,589.
Explanation
First, find the cube of 429, that is 78,998,589 Next, find the cube of 400, which is 64,000,000 Now, find the difference between them using the subtraction method. 78,998,589 – 64,000,000 = 14,998,589 Therefore, the 429³ is 14,998,589 larger than 400³.
Problem 4
If a cube with a side length of 429 cm is compared to a cube with a side length of 29 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 429 cm is 78,998,589 cm³
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object). Cubing 429 means multiplying 429 by itself three times: 429 × 429 = 184,041, and the 184,041 × 429 = 78,998,589. The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube. Therefore, the volume of the cube is 78,998,589 cm³.
Problem 5
Estimate the cube of 428.9 using the cube of 429.
The cube of 428.9 is approximately 78,998,589.
Explanation
First, identify the cube of 429, The cube of 429 is 429³ = 78,998,589. Since 428.9 is only a tiny bit less than 429, the cube of 428.9 will be almost the same as the cube of 429. The cube of 428.9 is approximately 78,998,589 because the difference between 428.9 and 429 is very small. So, we can approximate the value as 78,998,589.
FAQs on Cube of 429
1.What are the perfect cubes up to 429?
2.How do you calculate 429³?
3.What is the meaning of 429³?
4.What is the cube root of 429?
5.Is 429 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 429?
8.How do technology and digital tools in United States support learning Algebra and Cube of 429?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for Cube of 429
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 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 cube of its side length.
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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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