114 LearnersLast updated on May 28th, 2025
Cube of 71
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 71.
Cube of 71
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 71 can be written as 71³, which is the exponential form.
Or it can also be written in arithmetic form as, 71 × 71 × 71.
How to Calculate the Value of Cube of 71
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 kids to cube the numbers faster and easier without feeling confused or stuck while evaluating the answers.
- By Multiplication Method
- Using a Formula (a3)
- Using a Calculator
By Multiplication Method
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. 71³ = 71 × 71 × 71
Step 2: You get 357,911 as the answer.
Hence, the cube of 71 is 357,911.
Using a Formula (a³)
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 71 into two parts, as 70 and 1. Let a = 70 and b = 1, so a + b = 71
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 70³ 3a²b = 3 × 70² × 1 3ab² = 3 × 70 × 1² b³ = 1³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (70 + 1)³ = 70³ + 3 × 70² × 1 + 3 × 70 × 1² + 1³ 71³ = 343,000 + 14,700 + 210 + 1 71³ = 357,911
Step 5: Hence, the cube of 71 is 357,911.
Using a Calculator
To find the cube of 71 using a calculator, input the number 71 and use the cube function (if available) or multiply 71 × 71 × 71. This operation calculates the value of 71³, resulting in 357,911. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 7 followed by 1
Step 3: If the calculator has a cube function, press it to calculate 71³.
Step 4: If there is no cube function on the calculator, simply multiply 71 three times manually.
Step 5: The calculator will display 357,911.
Tips and Tricks for the Cube of 71
- 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.
Common Mistakes to Avoid When Calculating the Cube of 71
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:
Mistake 1
Incorrect Multiplication
Kids might multiply the numbers only twice. That is, 71 × 71 and not 71 × 71 × 71. Always remember that 71³ = 71 × 71 × 71.
Solved Examples on Cube of 71
Problem 1
What is the cube and cube root of 71?
The cube of 71 is 357,911 and the cube root of 71 is approximately 4.141.
Explanation
First, let’s find the cube of 71.
We know that the cube of a number is such that x³ = y,
Where x is the given number, and y is the cubed value of that number.
So, we get 71³ = 357,911. Next, we must find the cube root of 71.
We know that the cube root of a number ‘x’ is such that ∛x = y,
Where ‘x’ is the given number, and y is the cube root value of the number.
So, we get ∛71 ≈ 4.141.
Hence the cube of 71 is 357,911 and the cube root of 71 is approximately 4.141.
Problem 2
If the side length of the cube is 71 cm, what is the volume?
The volume is 357,911 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 71 for the side length: V = 71³ = 357,911 cm³.
Problem 3
How much larger is 71³ than 61³?
71³ – 61³ = 260,591.
Explanation
First find the cube of 71³, that is 357,911.
Next, find the cube of 61³, which is 97,320.
Now, find the difference between them using the subtraction method. 357,911 – 97,320 = 260,591.
Therefore, 71³ is 260,591 larger than 61³.
Problem 4
If a cube with a side length of 71 cm is compared to a cube with a side length of 11 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 71 cm is 357,911 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 71 means multiplying 71 by itself three times: 71 × 71 = 5,041, and then 5,041 × 71 = 357,911.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 357,911 cm³.
Problem 5
Estimate the cube of 70.9 using the cube of 71.
The cube of 70.9 is approximately 357,911.
Explanation
First, identify the cube of 71. The cube of 71 is 71³ = 357,911.
Since 70.9 is only a tiny bit less than 71, the cube of 70.9 will be almost the same as the cube of 71.
The cube of 70.9 is approximately 357,911 because the difference between 70.9 and 71 is very small.
So, we can approximate the value as 357,911.
FAQs on Cube of 71
1.What are the perfect cubes up to 71?
2.How do you calculate 71³?
3.What is the meaning of 71³?
4.What is the cube root of 71?
5.Is 71 a perfect cube?
6.How does learning Algebra help students in Saudi Arabia make better decisions in daily life?
7.How can cultural or local activities in Saudi Arabia support learning Algebra topics such as Cube of 71?
8.How do technology and digital tools in Saudi Arabia support learning Algebra and Cube of 71?
9.Does learning Algebra support future career opportunities for students in Saudi Arabia?
Important Glossaries for Cube of 71
- Binomial Formula: It is an algebraic expression used to expand the powers of a number, written as (a + b)ⁿ, where ‘n’ is a positive integer raised to the base. The formula is used to find the square and cube of a number.
- Cube of a Number: Multiplying a number by itself three times is called the cube of a number.
- Exponential Form: It is a way of expressing numbers using a base and an exponent (or power), where the exponent value indicates how many times the base is multiplied by itself. For example, 2³ represents 2 × 2 × 2 equals 8.
- Perfect Cube: A number that can be expressed as the cube of an integer is called a perfect cube.
- Calculator Function: A feature in some calculators that allows users to find the cube of a number quickly without manual multiplication.
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Jaskaran Singh Saluja
About the Author
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.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
