Last updated on May 29th, 2025
When a number is multiplied by itself thrice, the resultant number is called the cube of a number. Cubing is used in comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of 397.
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 397 can be written as 397³, which is the exponential form.
Or it can also be written in arithmetic form as 397 × 397 × 397.
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 in cubing the numbers faster and easier without feeling confused or stuck while evaluating the answers.
The multiplication method is a process in mathematics used to find the product of a number by combining them through repeated multiplication. It is a fundamental operation that forms the basis for more complex mathematical concepts.
Step 1: Write down the cube of the given number. 397³ = 397 × 397 × 397
Step 2: You get 62,564,573 as the answer. Hence, the cube of 397 is 62,564,573.
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 397 into two parts, as a and b. Let a = 400 and b = -3, so a + b = 397
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 400³ 3a²b = 3 × 400² × (-3) 3ab² = 3 × 400 × (-3)² b³ = (-3)³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (400 - 3)³ = 400³ + 3 × 400² × (-3) + 3 × 400 × (-3)² + (-3)³ 397³ = 64,000,000 - 1,440,000 + 10,800 - 27 397³ = 62,564,573
Step 5: Hence, the cube of 397 is 62,564,573.
To find the cube of 397 using a calculator, input the number 397 and use the cube function (if available) or multiply 397 × 397 × 397. This operation calculates the value of 397³, resulting in 62,564,573. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Enter 397.
Step 3: If the calculator has a cube function, press it to calculate 397³.
Step 4: If there is no cube function on the calculator, simply multiply 397 three times manually.
Step 5: The calculator will display 62,564,573.
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:
What is the cube and cube root of 397?
The cube of 397 is 62,564,573 and the cube root of 397 is approximately 7.370.
First, let’s find the cube of 397.
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 397³ = 62,564,573
Next, we must find the cube root of 397
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√397 ≈ 7.370
Hence the cube of 397 is 62,564,573 and the cube root of 397 is approximately 7.370.
If the side length of the cube is 397 cm, what is the volume?
The volume is 62,564,573 cm³.
Use the volume formula for a cube V = Side³.
Substitute 397 for the side length: V = 397³ = 62,564,573 cm³.
How much larger is 397³ than 387³?
397³ – 387³ = 3,067,473.
First, find the cube of 397, which is 62,564,573.
Next, find the cube of 387, which is 59,497,100.
Now, find the difference between them using the subtraction method. 62,564,573 – 59,497,100 = 3,067,473.
Therefore, 397³ is 3,067,473 larger than 387³.
If a cube with a side length of 397 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 397 cm is 62,564,573 cm³.
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 397 means multiplying 397 by itself three times: 397 × 397 = 157,609, and then 157,609 × 397 = 62,564,573.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 62,564,573 cm³.
Estimate the cube of 396.9 using the cube of 397.
The cube of 396.9 is approximately 62,564,573.
First, identify the cube of 397,
The cube of 397 is 397³ = 62,564,573. Since 396.9 is only a tiny bit less than 397, the cube of 396.9 will be almost the same as the cube of 397.
The cube of 396.9 is approximately 62,564,573 because the difference between 396.9 and 397 is very small.
So, we can approximate the value as 62,564,573.
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.