Last updated on June 3rd, 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 270.
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 multiplying a negative number by itself three times results in a negative number.
The cube of 270 can be written as 270³, which is the exponential form.
Or it can also be written in arithmetic form as, 270 × 270 × 270.
To check whether a number is a cube number, we can use the following three methods: multiplication method, a factor formula (a³), or by using a calculator. These three methods will help to cube the numbers faster and easier without confusion or getting stuck while evaluating the answers.
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. 270³ = 270 × 270 × 270
Step 2: You get 19,683,000 as the answer. Hence, the cube of 270 is 19,683,000.
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 270 into two parts. Let a = 200 and b = 70, so a + b = 270
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 200³ 3a²b = 3 × 200² × 70 3ab² = 3 × 200 × 70² b³ = 70³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (200 + 70)³ = 200³ + 3 × 200² × 70 + 3 × 200 × 70² + 70³ 270³ = 8,000,000 + 8,400,000 + 2,940,000 + 343,000 270³ = 19,683,000
Step 5: Hence, the cube of 270 is 19,683,000.
To find the cube of 270 using a calculator, input the number 270 and use the cube function (if available) or multiply 270 × 270 × 270. This operation calculates the value of 270³, resulting in 19,683,000. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 2 followed by 7 and 0.
Step 3: If the calculator has a cube function, press it to calculate 270³.
Step 4: If there is no cube function on the calculator, simply multiply 270 three times manually.
Step 5: The calculator will display 19,683,000.
There are some typical errors that might occur during the process of cubing a number. Let us take a look at five major mistakes that might occur:
What is the cube and cube root of 270?
The cube of 270 is 19,683,000 and the cube root of 270 is approximately 6.497.
First, let’s find the cube of 270.
We know that the cube of a number is x³ = y, where x is the given number, and y is the cubed value of that number.
So, we get 270³ = 19,683,000.
Next, we must find the cube root of 270.
We know that the cube root of a number ‘x’ is ∛x = y, where x is the given number, and y is the cube root value of the number.
So, we get ∛270 ≈ 6.497. Hence the cube of 270 is 19,683,000 and the cube root of 270 is approximately 6.497.
If the side length of a cube is 270 cm, what is the volume?
The volume is 19,683,000 cm³.
Use the volume formula for a cube V = Side³.
Substitute 270 for the side length: V = 270³ = 19,683,000 cm³.
How much larger is 270³ than 200³?
270³ – 200³ = 11,683,000.
First, find the cube of 270³, which is 19,683,000.
Next, find the cube of 200³, which is 8,000,000.
Now, find the difference between them using the subtraction method. 19,683,000 – 8,000,000 = 11,683,000.
Therefore, 270³ is 11,683,000 larger than 200³.
If a cube with a side length of 270 cm is compared to a cube with a side length of 70 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 270 cm is 19,683,000 cm³.
To find its volume, multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 270 means multiplying 270 by itself three times: 270 × 270 = 72,900, and 72,900 × 270 = 19,683,000.
The unit of volume is cubic centimeters (cm³) because we are calculating the space inside the cube.
Therefore, the volume of the cube is 19,683,000 cm³.
Estimate the cube of 269.9 using the cube of 270.
The cube of 269.9 is approximately 19,683,000.
First, identify the cube of 270.
The cube of 270 is 270³ = 19,683,000.
Since 269.9 is only a tiny bit less than 270, the cube of 269.9 will be almost the same as the cube of 270.
The cube of 269.9 is approximately 19,683,000 because the difference between 269.9 and 270 is very small.
So, we can approximate the value as 19,683,000.
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.