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 the cube of 675.
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 675 can be written as 675³, which is the exponential form. Or it can also be written in arithmetic form as, 675 × 675 × 675.
In order to check whether a number is a cube number or not, we can use the following three methods: 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. 675³ = 675 × 675 × 675
Step 2: You get 307,546,875 as the answer. Hence, the cube of 675 is 307,546,875.
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 675 into two parts, as 600 and 75. Let a = 600 and b = 75, so a + b = 675
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term
a³ = 600³
3a²b = 3 × 600² × 75
3ab² = 3 × 600 × 75²
b³ = 75³
Step 4: Add all the terms together:
(a + b)³ = a³ + 3a²b + 3ab² + b³
(600 + 75)³ = 600³ + 3 × 600² × 75 + 3 × 600 × 75² + 75³
675³ = 216,000,000 + 81,000,000 + 20,250,000 + 421,875
675³ = 307,546,875
Step 5: Hence, the cube of 675 is 307,546,875.
To find the cube of 675 using a calculator, input the number 675 and use the cube function (if available) or multiply 675 × 675 × 675. This operation calculates the value of 675³, resulting in 307,546,875. 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 5
Step 3: If the calculator has a cube function, press it to calculate 675³.
Step 4: If there is no cube function on the calculator, simply multiply 675 three times manually.
Step 5: The calculator will display 307,546,875.
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 675?
The cube of 675 is 307,546,875 and the cube root of 675 is approximately 8.781.
First, let’s find the cube of 675.
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 675³ = 307,546,875
Next, we must find the cube root of 675 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 ∛675 ≈ 8.781
Hence the cube of 675 is 307,546,875 and the cube root of 675 is approximately 8.781.
If the side length of the cube is 675 cm, what is the volume?
The volume is 307,546,875 cm³.
Use the volume formula for a cube V = Side³.
Substitute 675 for the side length: V = 675³ = 307,546,875 cm³.
How much larger is 675³ than 600³?
675³ – 600³ = 91,546,875.
First, find the cube of 675³, that is 307,546,875
Next, find the cube of 600³, which is 216,000,000
Now, find the difference between them using the subtraction method.
307,546,875 – 216,000,000 = 91,546,875
Therefore, 675³ is 91,546,875 larger than 600³.
If a cube with a side length of 675 cm is compared to a cube with a side length of 75 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 675 cm is 307,546,875 cm³.
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 675 means multiplying 675 by itself three times: 675 × 675 = 455,625, and then 455,625 × 675 = 307,546,875.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 307,546,875 cm³.
Estimate the cube 674.9 using the cube of 675.
The cube of 674.9 is approximately 307,546,875.
First, identify the cube of 675, The cube of 675 is 675³ = 307,546,875.
Since 674.9 is only a tiny bit less than 675, the cube of 674.9 will be almost the same as the cube of 675.
The cube of 674.9 is approximately 307,546,875 because the difference between 674.9 and 675 is very small.
So, we can approximate the value as 307,546,875.
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.