Last updated on June 5th, 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 725.
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 725 can be written as 725³, which is the exponential form. Or it can also be written in arithmetic form as 725 × 725 × 725.
In order to check whether a number is a cube number or not, we can use the following three methods: 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. 725³ = 725 × 725 × 725
Step 2: You get 381,078,125 as the answer. Hence, the cube of 725 is 381,078,125.
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 725 into two parts. Let a = 700 and b = 25, so a + b = 725.
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³.
Step 3: Calculate each term:
a³ = 700³
3a²b = 3 × 700² × 25
3ab² = 3 × 700 × 25²
b³ = 25³
Step 4: Add all the terms together:
(a + b)³ = a³ + 3a²b + 3ab² + b³
(700 + 25)³ = 700³ + 3 × 700² × 25 + 3 × 700 × 25² + 25³
725³ = 343,000,000 + 36,750,000 + 1,312,500 + 15,625
725³ = 381,078,125
Step 5: Hence, the cube of 725 is 381,078,125.
To find the cube of 725 using a calculator, input the number 725 and use the cube function (if available) or multiply 725 × 725 × 725. This operation calculates the value of 725³, resulting in 381,078,125. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Enter 725.
Step 3: If the calculator has a cube function, press it to calculate 725³.
Step 4: If there is no cube function on the calculator, simply multiply 725 three times manually.
Step 5: The calculator will display 381,078,125.
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 725?
The cube of 725 is 381,078,125, and the cube root of 725 is approximately 8.976.
First, let’s find the cube of 725.
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 725³ = 381,078,125
Next, we must find the cube root of 725 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 ∛725 ≈ 8.976
Hence the cube of 725 is 381,078,125, and the cube root of 725 is approximately 8.976.
If the side length of the cube is 725 cm, what is the volume?
The volume is 381,078,125 cm³.
Use the volume formula for a cube V = Side³.
Substitute 725 for the side length: V = 725³ = 381,078,125 cm³.
How much larger is 725³ than 625³?
725³ – 625³ = 254,828,125.
First find the cube of 725, which is 381,078,125
Next, find the cube of 625, which is 126,250,000
Now, find the difference between them using the subtraction method. 381,078,125 – 126,250,000 = 254,828,125
Therefore, 725³ is 254,828,125 larger than 625³.
If a cube with a side length of 725 cm is compared to a cube with a side length of 500 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 725 cm is 381,078,125 cm³.
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 725 means multiplying 725 by itself three times: 725 × 725 = 525,625, and then 525,625 × 725 = 381,078,125.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 381,078,125 cm³.
Estimate the cube of 724 using the cube of 725.
The cube of 724 is approximately 381,078,125.
First, identify the cube of 725, The cube of 725 is 725³ = 381,078,125.
Since 724 is only a tiny bit less than 725, the cube of 724 will be almost the same as the cube of 725.
The cube of 724 is approximately 381,078,125 because the difference between 724 and 725 is very small.
So, we can approximate the value as 381,078,125.
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.