100 LearnersLast updated on June 3rd, 2025
Cube of 137
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 137.
Cube of 137
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 multiplied by itself three times results in a negative number.
The cube of 137 can be written as 137³, which is the exponential form.
Or it can also be written in arithmetic form as 137 × 137 × 137.
How to Calculate the Value of Cube of 137
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 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. 137³ = 137 × 137 × 137
Step 2: You get 2,573,737 as the answer. Hence, the cube of 137 is 2,573,737.
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 137 into two parts, as a and b. Let a = 130 and b = 7, so a + b = 137
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 130³ 3a²b = 3 × 130² × 7 3ab² = 3 × 130 × 7² b³ = 7³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (130 + 7)³= 130³ + 3 × 130² × 7 + 3 × 130 × 7² + 7³ 137³ = 2,197,000 + 355,300 + 63,700 + 343 137³ = 2,573,737
Step 5: Hence, the cube of 137 is 2,573,737.
Using a Calculator
To find the cube of 137 using a calculator, input the number 137 and use the cube function (if available) or multiply 137 × 137 × 137. This operation calculates the value of 137³, resulting in 2,573,737. 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 3 and 7
Step 3: If the calculator has a cube function, press it to calculate 137³.
Step 4: If there is no cube function on the calculator, simply multiply 137 three times manually.
Step 5: The calculator will display 2,573,737.
Tips and Tricks for the Cube of 137
- 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 137
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 happen:
Mistake 1
Incorrect Multiplication
Multiplying the numbers only twice. That is, 137 × 137 and not 137 × 137 × 137. Always remember that 137³ = 137 × 137 × 137.
Solved Examples on Cube of 137
Problem 1
What is the cube and cube root of 137?
The cube of 137 is 2,573,737 and the cube root of 137 is approximately 5.152.
Explanation
First, let’s find the cube of 137.
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 137³ = 2,573,737 Next, we must find the cube root of 137
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√137 ≈ 5.152
Hence the cube of 137 is 2,573,737 and the cube root of 137 is approximately 5.152.
Problem 2
If the side length of the cube is 137 cm, what is the volume?
The volume is 2,573,737 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 137 for the side length: V = 137³ = 2,573,737 cm³.
Problem 3
How much larger is 137³ than 130³?
137³ – 130³ = 376,737.
Explanation
First find the cube of 137³, that is 2,573,737
Next, find the cube of 130³, which is 2,197,000
Now, find the difference between them using the subtraction method. 2,573,737 – 2,197,000 = 376,737
Therefore, 137³ is 376,737 larger than 130³.
Problem 4
If a cube with a side length of 137 cm is compared to a cube with a side length of 7 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 137 cm is 2,573,737 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 137 means multiplying 137 by itself three times: 137 × 137 = 18,769, and then 18,769 × 137 = 2,573,737.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 2,573,737 cm³.
Problem 5
Estimate the cube 136.9 using the cube 137.
The cube of 136.9 is approximately 2,573,737.
Explanation
First, identify the cube of 137,
The cube of 137 is 137³ = 2,573,737.
Since 136.9 is only a tiny bit less than 137, the cube of 136.9 will be almost the same as the cube of 137.
The cube of 136.9 is approximately 2,573,737 because the difference between 136.9 and 137 is very small.
So, we can approximate the value as 2,573,737.
FAQs on Cube of 137
1.What are the perfect cubes up to 137?
2.How do you calculate 137³?
3.What is the meaning of 137³?
4.What is the cube root of 137?
5.Is 137 a perfect cube?
6.How does learning Algebra help students in Thailand make better decisions in daily life?
7.How can cultural or local activities in Thailand support learning Algebra topics such as Cube of 137?
8.How do technology and digital tools in Thailand support learning Algebra and Cube of 137?
9.Does learning Algebra support future career opportunities for students in Thailand?
Important Glossaries for Cube of 137
- 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, which equals 8.
- Perfect Cube: A number that can be expressed as the cube of an integer. For instance, 8 is a perfect cube because it equals 2³.
- Volume of a Cube: The amount of space inside a cube, calculated using the formula V = side³, where 'side' is the length of one side of the cube.
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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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