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 401.
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 multiplying a negative number by itself three times results in a negative number.
The cube of 401 can be written as 4013, which is the exponential form.
Or it can also be written in arithmetic form as 401 × 401 × 401.
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 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. 4013 = 401 × 401 × 401
Step 2: Calculate the product to get 64,480,601 as the answer. Hence, the cube of 401 is 64,480,601.
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 401 into two parts. Let a = 400 and b = 1, so a + b = 401
Step 2: Now, apply the formula (a + b)3 = a3 + 3a2b + 3ab2 + b3
Step 3: Calculate each term a3 = 4003 3a2b = 3 × 4002 × 1 3ab2 = 3 × 400 × 12 b3 = 13
Step 4: Add all the terms together: (a + b)3 = a3 + 3a2b + 3ab2 + b3 (400 + 1)3 = 4003 + 3 × 4002 × 1 + 3 × 400 × 12 + 13 4013 = 64,000,000 + 480,000 + 1,200 + 1 4013 = 64,480,601
Step 5: Hence, the cube of 401 is 64,480,601.
To find the cube of 401 using a calculator, input the number 401 and use the cube function (if available) or multiply 401 × 401 × 401. This operation calculates the value of 4013, resulting in 64,480,601. 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 0 and 1
Step 3: If the calculator has a cube function, press it to calculate 4013.
Step 4: If there is no cube function on the calculator, simply multiply 401 three times manually.
Step 5: The calculator will display 64,480,601.
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 401?
The cube of 401 is 64,480,601 and the cube root of 401 is approximately 7.368.
First, let’s find the cube of 401.
We know that the cube of a number x is x3.
So, we get 4013 = 64,480,601. Next, we must find the cube root of 401.
We know that the cube root of a number x is ∛x.
So, we get ∛401 ≈ 7.368.
Hence, the cube of 401 is 64,480,601 and the cube root of 401 is approximately 7.368.
If the side length of a cube is 401 cm, what is the volume?
The volume is 64,480,601 cm³.
Use the volume formula for a cube V = Side3.
Substitute 401 for the side length: V = 4013 = 64,480,601 cm³.
How much larger is 401^3 than 400^3?
4013 – 4003 = 481,201.
First find the cube of 401, which is 64,480,601.
Next, find the cube of 400, which is 64,000,000.
Now, find the difference between them using the subtraction method. 64,480,601 – 64,000,000 = 481,201.
Therefore, 401^3 is 481,201 larger than 4003.
If a cube with a side length of 401 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 401 cm is 64,480,601 cm³.
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 401 means multiplying 401 by itself three times: 401 × 401 = 160,801, and then 160,801 × 401 = 64,480,601.
The unit of volume is cubic centimeters (cm³) because we are calculating the space inside the cube.
Therefore, the volume of the cube is 64,480,601 cm³.
Estimate the cube of 400.1 using the cube of 401.
The cube of 400.1 is approximately 64,480,601.
First, identify the cube of 401.
The cube of 401 is 4013 = 64,480,601.
Since 400.1 is only a tiny bit less than 401, the cube of 400.1 will be almost the same as the cube of 401.
The cube of 400.1 is approximately 64,480,601 because the difference between 400.1 and 401 is very small.
So, we can approximate the value as 64,480,601.
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.