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 while comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about cubes of 461.
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 461 can be written as 461³, which is the exponential form. Or it can also be written in arithmetic form as, 461 × 461 × 461.
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.
461³ = 461 × 461 × 461
Step 2: You get 98,373,581 as the answer.
Hence, the cube of 461 is 98,373,581.
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 461 into two parts.
Let a = 460 and b = 1, so a + b = 461
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term
a³ = 460³
3a²b = 3 × 460² × 1
3ab² = 3 × 460 × 1²
b³ = 1³
Step 4: Add all the terms together:
(a + b)³ = a³ + 3a²b + 3ab² + b³
(460 + 1)³ = 460³ + 3 × 460² × 1 + 3 × 460 × 1² + 1³
461³ = 97,336,000 + 634,800 + 1,380 + 1
461³ = 98,373,581
Step 5: Hence, the cube of 461 is 98,373,581.
To find the cube of 461 using a calculator, input the number 461 and use the cube function (if available) or multiply 461 × 461 × 461. This operation calculates the value of 461³, resulting in 98,373,581. 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 6 and 1.
Step 3: If the calculator has a cube function, press it to calculate 461³.
Step 4: If there is no cube function on the calculator, simply multiply 461 three times manually.
Step 5: The calculator will display 98,373,581.
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 461?
The cube of 461 is 98,373,581 and the cube root of 461 is approximately 7.77.
First, let’s find the cube of 461.
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 461³ = 98,373,581.
Next, we must find the cube root of 461.
We know that cube root of a number ‘x’, such that ³√x = y.
Where ‘x’ is the given number, and y is the cube root value of the number.
So, we get ³√461 = approximately 7.77
Hence the cube of 461 is 98,373,581 and the cube root of 461 is approximately 7.77.
If the side length of the cube is 461 cm, what is the volume?
The volume is 98,373,581 cm³.
Use the volume formula for a cube V = Side³.
Substitute 461 for the side length: V = 461³ = 98,373,581 cm³.
How much larger is 461³ than 360³?
461³ – 360³ = 87,443,021.
First, find the cube of 461, that is 98,373,581.
Next, find the cube of 360, which is 46,656,000
Now, find the difference between them using the subtraction method.
98,373,581 – 10,930,560 = 87,443,021
Therefore, 461³ is 87,443,021 larger than 360³.
If a cube with a side length of 461 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 461 cm is 98,373,581 cm³.
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 461 means multiplying 461 by itself three times: 461 × 461 = 212,521, and then 212,521 × 461 = 98,373,581.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 98,373,581 cm³.
Estimate the cube 460.9 using the cube 461.
The cube of 460.9 is approximately 98,373,581.
First, identify the cube of 461.
The cube of 461 is 461³ = 98,373,581.
Since 460.9 is only a tiny bit less than 461, the cube of 460.9 will be almost the same as the cube of 461.
The cube of 460.9 is approximately 98,373,581 because the difference between 460.9 and 461 is very small.
So, we can approximate the value as 98,373,581.
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.