Last updated on May 28th, 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 471.
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 471 can be written as 471³, which is the exponential form. Or it can also be written in arithmetic form as, 471 × 471 × 471.
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 you 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. 471³ = 471 × 471 × 471
Step 2: You get 104,775,111 as the answer. Hence, the cube of 471 is 104,775,111.
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 471 into two parts. Let a = 470 and b = 1, so a + b = 471
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³= 470³ 3a²b = 3 × 470² × 1 3ab² = 3 × 470 × 1² b³ = 1³
Step 4: Add all the terms together:
(a + b)³ = a³ + 3a²b + 3ab² + b³
(470 + 1)³= 470³ + 3 × 470² × 1 + 3 × 470 × 1² + 1³
471³ = 103,823,000 + 661,800 + 1,410 + 1
471³ = 104,775,111
Step 5: Hence, the cube of 471 is 104,775,111.
To find the cube of 471 using a calculator, input the number 471 and use the cube function (if available) or multiply 471 × 471 × 471. This operation calculates the value of 471³, resulting in 104,775,111. 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 7 and 1
Step 3: If the calculator has a cube function, press it to calculate 471³.
Step 4: If there is no cube function on the calculator, simply multiply 471 three times manually.
Step 5: The calculator will display 104,775,111.
There are some typical errors that might occur during the process of cubing a number. Let us take a look at five of the major mistakes:
What is the cube and cube root of 471?
The cube of 471 is 104,775,111 and the cube root of 471 is approximately 7.769.
First, let’s find the cube of 471.
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 471³= 104,775,111
Next, we must find the cube root of 471 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 ∛471 ≈ 7.769
Hence the cube of 471 is 104,775,111 and the cube root of 471 is approximately 7.769.
If the side length of the cube is 471 cm, what is the volume?
The volume is 104,775,111 cm³.
Use the volume formula for a cube V = Side³.
Substitute 471 for the side length: V = 471³ = 104,775,111 cm³.
How much larger is 471³ than 370³?
471³ – 370³ = 51,787,211.
First find the cube of 471, that is 104,775,111
Next, find the cube of 370, which is 52,987,900 Now, find the difference between them using the subtraction method.
104,775,111 – 52,987,900 = 51,787,211
Therefore, 471³ is 51,787,211 larger than 370³.
If a cube with a side length of 471 cm is compared to a cube with a side length of 21 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 471 cm is 104,775,111 cm³.
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 471 means multiplying 471 by itself three times: 471 × 471 = 221,841, and then 221,841 × 471 = 104,775,111.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 104,775,111 cm³.
Estimate the cube of 470.5 using the cube of 471.
The cube of 470.5 is approximately 104,775,111.
First, identify the cube of 471, The cube of 471 is 471³ = 104,775,111.
Since 470.5 is only a tiny bit less than 471, the cube of 470.5 will be almost the same as the cube of 471.
The cube of 470.5 is approximately 104,775,111 because the difference between 470.5 and 471 is very small.
So, we can approximate the value as 104,775,111.
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.