Last updated on June 30th, 2025
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 1297.
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 1297 can be written as 1297³, which is the exponential form. Or it can also be written in arithmetic form as 1297 × 1297 × 1297.
In order to check whether a number is a cube number or not, we can use the following three methods, such as the multiplication method, a factor formula (a³), or by using a calculator.
These three methods will help calculate the cube of numbers faster and easier without feeling confused or stuck while evaluating the answers.
By Multiplication Method Using a Formula Using a Calculator
The multiplication method is a process in mathematics used to find the product of 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. 1297³ = 1297 × 1297 × 1297
Step 2: Perform the multiplication to get the answer. Hence, the cube of 1297 is 2,180,707,473.
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 1297 into two parts, as a and b. Let a = 1300 and b = -3, so a + b = 1297
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 1300³ 3a²b = 3 × 1300² × (-3) 3ab² = 3 × 1300 × (-3)² b³ = (-3)³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (1300 - 3)³ = 1300³ + 3 × 1300² × (-3) + 3 × 1300 × 9 + (-27) 1297³ = 2,197,000,000 - 15,210,000 + 35,100 - 27 1297³ = 2,180,707,473
Step 5: Hence, the cube of 1297 is 2,180,707,473.
To find the cube of 1297 using a calculator, input the number 1297 and use the cube function (if available) or multiply 1297 × 1297 × 1297.
This operation calculates the value of 1297³, resulting in 2,180,707,473.
It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Input 1297
Step 3: If the calculator has a cube function, press it to calculate 1297³.
Step 4: If there is no cube function on the calculator, simply multiply 1297 three times manually.
Step 5: The calculator will display 2,180,707,473. 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.
There are some typical errors that individuals might make during the process of cubing a number.
Let us take a look at five of the major mistakes that might occur:
What is the cube and cube root of 1297?
The cube of 1297 is 2,180,707,473 and the cube root of 1297 is approximately 10.861.
First, let’s find the cube of 1297. 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 1297³ = 2,180,707,473. Next, we must find the cube root of 1297.
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 ∛1297 ≈ 10.861.
Hence, the cube of 1297 is 2,180,707,473 and the cube root of 1297 is approximately 10.861.
If the side length of the cube is 1297 cm, what is the volume?
The volume is 2,180,707,473 cm³.
Use the volume formula for a cube V = Side³. Substitute 1297 for the side length: V = 1297³ = 2,180,707,473 cm³.
How much larger is 1297³ than 1000³?
1297³ – 1000³ = 1,180,707,473.
First, find the cube of 1297³, that is 2,180,707,473. Next, find the cube of 1000³, which is 1,000,000,000.
Now, find the difference between them using the subtraction method. 2,180,707,473 – 1,000,000,000 = 1,180,707,473.
Therefore, 1297³ is 1,180,707,473 larger than 1000³.
If a cube with a side length of 1297 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 1297 cm is 2,180,707,473 cm³.
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 1297 means multiplying 1297 by itself three times: 1297 × 1297 = 1,682,209, and then 1,682,209 × 1297 = 2,180,707,473.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 2,180,707,473 cm³.
Estimate the cube of 1300 using the cube of 1297.
The cube of 1300 is approximately 2,197,000,000.
First, identify the cube of 1297. The cube of 1297 is 1297³ = 2,180,707,473.
Since 1300 is only slightly larger than 1297, the cube of 1300 will be slightly larger than the cube of 1297.
The cube of 1300 is approximately 2,197,000,000 because the difference between 1297 and 1300 is small.
So, we can approximate the value as 2,197,000,000.
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.
: He loves to play the quiz with kids through algebra to make kids love it.