101 LearnersLast updated on May 26th, 2025
Cube of 172
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 172.
Cube of 172
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 172 can be written as 172³, which is the exponential form. Or it can also be written in arithmetic form as, 172 × 172 × 172.
How to Calculate the Value of Cube of 172
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.
- By Multiplication Method
- Using a Formula
- 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. 172³ = 172 × 172 × 172
Step 2: You get 5,083,648 as the answer. Hence, the cube of 172 is 5,083,648.
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 172 into two parts, as 160 and 12. Let a = 160 and b = 12, so a + b = 172
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 160³ 3a²b = 3 × 160² × 12 3ab² = 3 × 160 × 12² b³ = 12³
Step 4: Add all the terms together:
(a + b)³ = a³ + 3a²b + 3ab² + b³
(160 + 12)³ = 160³ + 3 × 160² × 12 + 3 × 160 × 12² + 12³
172³ = 4,096,000 + 368,640 + 69,120 + 1,728
172³ = 5,083,488
Step 5: Hence, the cube of 172 is 5,083,648.
Using a Calculator
To find the cube of 172 using a calculator, input the number 172 and use the cube function (if available) or multiply 172 × 172 × 172. This operation calculates the value of 172³, resulting in 5,083,648. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 1 followed by 7 and then 2
Step 3: If the calculator has a cube function, press it to calculate 172³.
Step 4: If there is no cube function on the calculator, simply multiply 172 three times manually.
Step 5: The calculator will display 5,083,648.
Tips and Tricks for the Cube of 172
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 172
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, 172 × 172 and not 172 × 172 × 172. Always remember that 172³ = 172 × 172 × 172.
Solved Examples on Cube of 172
Problem 1
What is the cube and cube root of 172?
The cube of 172 is 5,083,648 and the cube root of 172 is approximately 5.541.
Explanation
First, let’s find the cube of 172.
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 172³ = 5,083,648
Next, we must find the cube root of 172 We know that the 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√172 ≈ 5.541 Hence the cube of 172 is 5,083,648 and the cube root of 172 is approximately 5.541.
Problem 2
If the side length of the cube is 172 cm, what is the volume?
The volume is 5,083,648 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 172 for the side length: V = 172³ = 5,083,648 cm³.
Problem 3
How much larger is 172³ than 160³?
172³ – 160³ = 987,648.
Explanation
First find the cube of 172³, that is 5,083,648 Next, find the cube of 160³, which is 4,096,000
Now, find the difference between them using the subtraction method.
5,083,648 – 4,096,000 = 987,648
Therefore, 172³ is 987,648 larger than 160³.
Problem 4
If a cube with a side length of 172 cm is compared to a cube with a side length of 12 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 172 cm is 5,083,648 cm³
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 172 means multiplying 172 by itself three times: 172 × 172 = 29,584, and then 29,584 × 172 = 5,083,648.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 5,083,648 cm³.
Problem 5
Estimate the cube of 171.9 using the cube of 172.
The cube of 171.9 is approximately 5,083,648.
Explanation
First, identify the cube of 172, The cube of 172 is 172³ = 5,083,648.
Since 171.9 is only a tiny bit less than 172, the cube of 171.9 will be almost the same as the cube of 172.
The cube of 171.9 is approximately 5,083,648 because the difference between 171.9 and 172 is very small.
So, we can approximate the value as 5,083,648.
FAQs on Cube of 172
1.What are the perfect cubes up to 172?
2.How do you calculate 172³?
3.What is the meaning of 172³?
4.What is the cube root of 172?
5.Is 172 a perfect cube?
6.How does learning Algebra help students in Australia make better decisions in daily life?
7.How can cultural or local activities in Australia support learning Algebra topics such as Cube of 172?
8.How do technology and digital tools in Australia support learning Algebra and Cube of 172?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for Cube of 172
- 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.
- Cube Root: The cube root of a number is a value that, when multiplied by itself three times, gives the original number.
- Volume of a Cube: It is the amount of space occupied by a cube, calculated by cubing the side length of the cube.
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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.
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