Last updated on June 2nd, 2025
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 424.
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 424 can be written as 4243, which is the exponential form.
Or it can also be written in arithmetic form as, 424 × 424 × 424.
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 students cube numbers faster and easier without feeling confused or stuck while evaluating the answers.
The multiplication method is a process in mathematics used to find the product of numbers by combining them through repeated multiplication. It is a fundamental operation that forms the basis for more complex mathematical concepts.
Step 1: Write down the cube of the given number. 4243 = 424 × 424 × 424
Step 2: You get 76,336,064 as the answer. Hence, the cube of 424 is 76,336,064.
The formula (a + b)3is a binomial formula for finding the cube of a number. The formula is expanded as \(a3 + 3a2b + 3ab2 + b3.
Step 1: Split the number 424 into two parts. Let a = 400 and b = 24, so a + b = 424
Step 2: Now, apply the formula (a + b)3 = a3 + 3a2b + 3ab2 + b3
Step 3: Calculate each term a3 = 4003 3a2b = 3 × 4002 × 24 3ab2 = 3 × 400 × 242 b3 = 243
Step 4: Add all the terms together: (a + b)3 = a3 + 3a2b + 3ab2 + b3 (400 + 24)3 = 4003 + 3 × 4002 × 24 + 3 × 400 × 242 + 243 4243 = 64,000,000 + 11,520,000 + 691,200 + 13,824 4243 = 76,336,064
Step 5: Hence, the cube of 424 is 76,336,064.
To find the cube of 424 using a calculator, input the number 424 and use the cube function (if available) or multiply 424 × 424 × 424. This operation calculates the value of 4243, resulting in 76,336,064. 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 4
Step 3: If the calculator has a cube function, press it to calculate 4243.
Step 4: If there is no cube function on the calculator, simply multiply 424 three times manually.
Step 5: The calculator will display 76,336,064.
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.
There are some typical errors that students might make during the process of cubing a number. Let us take a look at five of the major mistakes that students might make:
What is the cube and cube root of 424?
The cube of 424 is 76,336,064 and the cube root of 424 is approximately 7.506.
First, let’s find the cube of 424.
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 4243 = 76,336,064 Next, we must find the cube root of 424
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 ∛424 ≈ 7.506
Hence the cube of 424 is 76,336,064 and the cube root of 424 is approximately 7.506.
If the side length of the cube is 424 cm, what is the volume?
The volume is 76,336,064 cm³.
Use the volume formula for a cube V = Side3.
Substitute 424 for the side length: V = 4243 = 76,336,064cm³.
How much larger is \(424^3\) than \(400^3\)?
\(4243 - 4003 = 12,336,064\).
First, find the cube of 4243, that is 76,336,064
Next, find the cube of 4003, which is 64,000,000
Now, find the difference between them using the subtraction method. 76,336,064 - 64,000,000 = 12,336,064
Therefore, 4243 is 12,336,064 larger than 4003.
If a cube with a side length of 424 cm is compared to a cube with a side length of 24 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 424 cm is 76,336,064 cm³.
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 424 means multiplying 424 by itself three times: 424 × 424 = 179,776, and 179,776 × 424 = 76,336,064.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 76,336,064 cm³.
Estimate the cube of 425 using the cube of 424.
The cube of 425 is approximately 76,336,064.
First, identify the cube of 424,
The cube of 424 is 4243 = 76,336,064.
Since 425 is only slightly more than 424, the cube of 425 will be almost the same as the cube of 424.
The cube of 425 is approximately 76,336,064 because the difference between 424 and 425 is very small.
So, we can approximate the value as 76,336,064.
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.
: He loves to play the quiz with kids through algebra to make kids love it.