Last updated on June 2nd, 2025
When a number is multiplied by itself thrice, the resultant number is called the cube of a number. Cubing is used while comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about cubes of 670.
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 670 can be written as 670³, which is the exponential form. Or it can also be written in arithmetic form as 670 × 670 × 670.
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 kids to cube 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 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. 670³ = 670 × 670 × 670
Step 2: You get 301,716,300 as the answer. Hence, the cube of 670 is 301,716,300.
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 670 into two parts, as and . Let a = 600 and b = 70, so a + b = 670
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 600³ 3a²b = 3 × 600² × 70 3ab² = 3 × 600 × 70² b³ = 70³
Step 4: Add all the terms together:
(a + b)³ = a³ + 3a²b + 3ab² + b³
(600 + 70)³ = 600³ + 3 × 600² × 70 + 3 × 600 × 70² + 70³
670³ = 216,000,000 + 75,600,000 + 8,820,000 + 343,000
670³ = 301,716,300
Step 5: Hence, the cube of 670 is 301,716,300.
To find the cube of 670 using a calculator, input the number 670 and use the cube function (if available) or multiply 670 × 670 × 670. This operation calculates the value of 670³, resulting in 301,716,300. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 6 followed by 7 and then 0
Step 3: If the calculator has a cube function, press it to calculate 670³.
Step 4: If there is no cube function on the calculator, simply multiply 670 three times manually.
Step 5: The calculator will display 301,716,300.
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:
What is the cube and cube root of 670?
The cube of 670 is 301,716,300 and the cube root of 670 is approximately 8.742.
First, let’s find the cube of 670. We know that the cube of a number is such that x³ = y, where x is the given number, and y is the cubed value of that number.
So, we get 670³ = 301,716,300.
Next, we must find the cube root of 670. 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√670 ≈ 8.742.
Hence, the cube of 670 is 301,716,300 and the cube root of 670 is approximately 8.742.
If the side length of the cube is 670 cm, what is the volume?
The volume is 301,716,300 cm³.
Use the volume formula for a cube V = Side³.
Substitute 670 for the side length: V = 670³ = 301,716,300 cm³.
How much larger is 670³ than 600³?
670³ – 600³ = 85,716,300.
First, find the cube of 670³, which is 301,716,300.
Next, find the cube of 600³, which is 216,000,000.
Now, find the difference between them using the subtraction method.
301,716,300 – 216,000,000 = 85,716,300.
Therefore, 670³ is 85,716,300 larger than 600³.
If a cube with a side length of 670 cm is compared to a cube with a side length of 200 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 670 cm is 301,716,300 cm³.
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 670 means multiplying 670 by itself three times: 670 × 670 = 448,900, and then 448,900 × 670 = 301,716,300.
The unit of volume is cubic centimeters (cm³) because we are calculating the space inside the cube.
Therefore, the volume of the cube is 301,716,300 cm³.
Estimate the cube 669.9 using the cube 670.
The cube of 669.9 is approximately 301,716,300.
First, identify the cube of 670.
The cube of 670 is 670³ = 301,716,300.
Since 669.9 is only a tiny bit less than 670, the cube of 669.9 will be almost the same as the cube of 670.
The cube of 669.9 is approximately 301,716,300 because the difference between 669.9 and 670 is very small.
So, we can approximate the value as 301,716,300.
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.