Last updated on May 30th, 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 cubes of 420.
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 420 can be written as 4203, which is the exponential form.
Or it can also be written in arithmetic form as, 420 × 420 × 420.
In order to check whether a number is a cube number or not, we can use the following three methods, such as 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.
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. 4203 = 420 × 420 × 420
Step 2: You get 74,088,000 as the answer. Hence, the cube of 420 is 74,088,000.
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 420 into two parts, as and . Let a = 400 and b = 20, so a + b = 420
Step 2: Now, apply the formula (a + b)3 = a3 + 3a2b + 3ab2 + b3
Step 3: Calculate each term a3 = 4003 3a2b = 3 × 4002 × 20 3ab2 = 3 × 400 × 202 b3 = 203
Step 4: Add all the terms together: (a + b)3 = a3 + 3a2b + 3ab2 + b3 (400 + 20)3 = 4003 + 3 × 4002 × 20 + 3 × 400 × 202 + 203 4203 = 64,000,000 + 9,600,000 + 960,000 + 8,000 4203 = 74,088,000
Step 5: Hence, the cube of 420 is 74,088,000.
To find the cube of 420 using a calculator, input the number 420 and use the cube function (if available) or multiply 420 × 420 × 420. This operation calculates the value of 4203, resulting in 74,088,000. 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 0
Step 3: If the calculator has a cube function, press it to calculate 4203.
Step 4: If there is no cube function on the calculator, simply multiply 420 three times manually.
Step 5: The calculator will display 74,088,000.
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 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:
What is the cube and cube root of 420?
The cube of 420 is 74,088,000 and the cube root of 420 is approximately 7.476.
First, let’s find the cube of 420.
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 4203 = 74,088,000
Next, we must find the cube root of 420
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 ∛420} ≈ 7.476
Hence the cube of 420 is 74,088,000 and the cube root of 420 is approximately 7.476.
If the side length of the cube is 420 cm, what is the volume?
The volume is 74,088,000 cm³.
Use the volume formula for a cube V = Side3.
Substitute 420 for the side length: V = 4203 = 74,088,000cm³.
How much larger is \(420^3\) than \(400^3\)?
4203 - 4003 = 10,088,000.
First, find the cube of 4203, that is 74,088,000
Next, find the cube of 4003, which is 64,000,000
Now, find the difference between them using the subtraction method. 74,088,000 - 64,000,000 = 10,088,000
Therefore, the 4203 is 10,088,000 larger than 4003.
If a cube with a side length of 420 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 420 cm is 74,088,000 cm³
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 420 means multiplying 420 by itself three times: 420 × 420 = 176,400, and then 176,400 × 420 = 74,088,000.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 74,088,000 cm³.
Estimate the cube of 419.9 using the cube of 420.
The cube of 419.9 is approximately 74,088,000.
First, identify the cube of 420, The cube of 420 is 4203 = 74,088,000.
Since 419.9 is only a tiny bit less than 420, the cube of 419.9 will be almost the same as the cube of 420.
The cube of 419.9 is approximately 74,088,000 because the difference between 419.9 and 420 is very small.
So, we can approximate the value as 74,088,000.
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.