100 LearnersLast updated on May 27th, 2025
Cube of 907
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 907.
Cube of 907
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 907 can be written as 907³, which is the exponential form. Or it can also be written in arithmetic form as, 907 × 907 × 907.
How to Calculate the Value of Cube of 907
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. 907³ = 907 × 907 × 907 Step 2: You get 746,071,043 as the answer. Hence, the cube of 907 is 746,071,043.
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 907 into two parts. Let a = 900 and b = 7, so a + b = 907 Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³ Step 3: Calculate each term a³ = 900³ 3a²b = 3 × 900² × 7 3ab² = 3 × 900 × 7² b³ = 7³ Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (900 + 7)³ = 900³ + 3 × 900² × 7 + 3 × 900 × 7² + 7³ 907³ = 729,000,000 + 170,100 + 132,300 + 343 907³ = 746,071,043 Step 5: Hence, the cube of 907 is 746,071,043.
Using a Calculator
To find the cube of 907 using a calculator, input the number 907 and use the cube function (if available) or multiply 907 × 907 × 907. This operation calculates the value of 907³, resulting in 746,071,043. It’s a quick way to determine the cube without manual computation. Step 1: Ensure the calculator is functioning properly. Step 2: Press 9, 0, 7 in sequence. Step 3: If the calculator has a cube function, press it to calculate 907³. Step 4: If there is no cube function on the calculator, simply multiply 907 three times manually. Step 5: The calculator will display 746,071,043.
Tips and Tricks for the Cube of 907
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 907
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, 907 × 907 and not 907 × 907 × 907. Always remember that 907³ = 907 × 907 × 907.
Solved Examples on Cube of 907
Problem 1
What is the cube and cube root of 907?
The cube of 907 is 746,071,043 and the cube root of 907 is approximately 9.67.
Explanation
First, let’s find the cube of 907. 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 907³ = 746,071,043. Next, we must find the cube root of 907. 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√907 ≈ 9.67. Hence the cube of 907 is 746,071,043 and the cube root of 907 is approximately 9.67.
Problem 2
If the side length of the cube is 907 cm, what is the volume?
The volume is 746,071,043 cm³.
Explanation
Use the volume formula for a cube V = Side³. Substitute 907 for the side length: V = 907³ = 746,071,043 cm³.
Problem 3
How much larger is 907³ than 900³?
907³ – 900³ = 1,071,043.
Explanation
First find the cube of 907, which is 746,071,043. Next, find the cube of 900, which is 729,000,000. Now, find the difference between them using the subtraction method. 746,071,043 – 729,000,000 = 1,071,043. Therefore, 907³ is 1,071,043 larger than 900³.
Problem 4
If a cube with a side length of 907 cm is compared to a cube with a side length of 100 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 907 cm is 746,071,043 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object). Cubing 907 means multiplying 907 by itself three times: 907 × 907 = 822,649, and then 822,649 × 907 = 746,071,043. The unit of volume is cubic centimeters (cm³) because we are calculating the space inside the cube. Therefore, the volume of the cube is 746,071,043 cm³.
Problem 5
Estimate the cube 906.9 using the cube 907.
The cube of 906.9 is approximately 746,071,043.
Explanation
First, identify the cube of 907. The cube of 907 is 907³ = 746,071,043. Since 906.9 is only a tiny bit less than 907, the cube of 906.9 will be almost the same as the cube of 907. The cube of 906.9 is approximately 746,071,043 because the difference between 906.9 and 907 is very small. So, we can approximate the value as 746,071,043.
FAQs on Cube of 907
1.What are the perfect cubes up to 907?
2.How do you calculate 907³?
3.What is the meaning of 907³?
4.What is the cube root of 907?
5.Is 907 a perfect cube?
6.How does learning Algebra help students in Vietnam make better decisions in daily life?
7.How can cultural or local activities in Vietnam support learning Algebra topics such as Cube of 907?
8.How do technology and digital tools in Vietnam support learning Algebra and Cube of 907?
9.Does learning Algebra support future career opportunities for students in Vietnam?
Important Glossaries for Cube of 907
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. Volume of a Cube: The amount of space occupied by a cube, calculated as the side length raised to the power of three.
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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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