100 LearnersLast updated on May 26th, 2025
Cube of 173
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 173.
Cube of 173
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 173 can be written as 173³, which is the exponential form. Or it can also be written in arithmetic form as, 173 × 173 × 173.
How to Calculate the Value of Cube of 173
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 users 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. 173³ = 173 × 173 × 173
Step 2: You get 5,181,067 as the answer. Hence, the cube of 173 is 5,181,067.
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 173 into two parts, as 170 and 3. Let a = 170 and b = 3, so a + b = 173
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 170³ 3a²b = 3 × 170² × 3 3ab² = 3 × 170 × 3² b³ = 3³
Step 4: Add all the terms together:
(a + b)³ = a³ + 3a²b + 3ab² + b³
(170 + 3)³ = 170³ + 3 × 170² × 3 + 3 × 170 × 3² + 3³
173³ = 4,913,000 + 260,100 + 4,590 + 27
173³ = 5,181,067
Step 5: Hence, the cube of 173 is 5,181,067.
Using a Calculator
To find the cube of 173 using a calculator, input the number 173 and use the cube function (if available) or multiply 173 × 173 × 173. This operation calculates the value of 173³, resulting in 5,181,067. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 1, then 7, and then 3
Step 3: If the calculator has a cube function, press it to calculate 173³.
Step 4: If there is no cube function on the calculator, simply multiply 173 three times manually.
Step 5: The calculator will display 5,181,067.
Tips and Tricks for the Cube of 173
- 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 173
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 that might be made:
Mistake 1
Incorrect Multiplication
There might be a tendency to multiply the numbers only twice. That is, 173 × 173 and not 173 × 173 × 173. Always remember that 173³ = 173 × 173 × 173.
Solved Examples on Cube of 173
Problem 1
What is the cube and cube root of 173?
The cube of 173 is 5,181,067, and the cube root of 173 is approximately 5.545.
Explanation
First, let’s find the cube of 173.
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 173³ = 5,181,067.
Next, we must find the cube root of 173. We know that the 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 ∛173 ≈ 5.545.
Hence, the cube of 173 is 5,181,067, and the cube root of 173 is approximately 5.545.
Problem 2
If the side length of the cube is 173 cm, what is the volume?
The volume is 5,181,067 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 173 for the side length: V = 173³ = 5,181,067 cm³.
Problem 3
How much larger is 173³ than 170³?
173³ – 170³ = 268,067.
Explanation
First, find the cube of 173, which is 5,181,067.
Next, find the cube of 170, which is 4,913,000.
Now, find the difference between them using the subtraction method.
5,181,067 – 4,913,000 = 268,067.
Therefore, 173³ is 268,067 larger than 170³.
Problem 4
If a cube with a side length of 173 cm is compared to a cube with a side length of 3 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 173 cm is 5,181,067 cm³.
Explanation
To find its volume, multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 173 means multiplying 173 by itself three times: 173 × 173 = 29,929, and then 29,929 × 173 = 5,181,067.
The unit of volume is cubic centimeters (cm³) because we are calculating the space inside the cube.
Therefore, the volume of the cube is 5,181,067 cm³.
Problem 5
Estimate the cube of 172.9 using the cube of 173.
The cube of 172.9 is approximately 5,181,067.
Explanation
First, identify the cube of 173, The cube of 173 is 173³ = 5,181,067.
Since 172.9 is only a tiny bit less than 173, the cube of 172.9 will be almost the same as the cube of 173.
The cube of 172.9 is approximately 5,181,067 because the difference between 172.9 and 173 is very small.
So, we can approximate the value as 5,181,067.
FAQs on Cube of 173
1.What are the perfect cubes up to 173?
2.How do you calculate 173³?
3.What is the meaning of 173³?
4.What is the cube root of 173?
5.Is 173 a perfect cube?
6.How does learning Algebra help students in Indonesia make better decisions in daily life?
7.How can cultural or local activities in Indonesia support learning Algebra topics such as Cube of 173?
8.How do technology and digital tools in Indonesia support learning Algebra and Cube of 173?
9.Does learning Algebra support future career opportunities for students in Indonesia?
Important Glossaries for Cube of 173
- 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 product of three equal integers, such as 1, 8, or 27.
- Volume of a Cube: The amount of space occupied by a cube, calculated as the cube of its side length, V = Side³.
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Jaskaran Singh Saluja
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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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