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 while comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of 741.
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 741 can be written as 741³, which is the exponential form. Or it can also be written in arithmetic form as 741 × 741 × 741.
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 students 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. 741³ = 741 × 741 × 741
Step 2: You get 406,573,821 as the answer. Hence, the cube of 741 is 406,573,821.
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 741 into two parts. Let a = 700 and b = 41, so a + b = 741
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 700³ 3a²b = 3 × 700² × 41 3ab² = 3 × 700 × 41² b³ = 41³
Step 4: Add all the terms together:
(a + b)³ = a³ + 3a²b + 3ab² + b³
(700 + 41)³ = 700³ + 3 × 700² × 41 + 3 × 700 × 41² + 41³
741³ = 343,000,000 + 60,060,000 + 3,528,300 + 68,921
741³ = 406,573,821
Step 5: Hence, the cube of 741 is 406,573,821.
To find the cube of 741 using a calculator, input the number 741 and use the cube function (if available) or multiply 741 × 741 × 741. This operation calculates the value of 741³, resulting in 406,573,821. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Enter 7, 4, 1
Step 3: If the calculator has a cube function, press it to calculate 741³.
Step 4: If there is no cube function on the calculator, simply multiply 741 three times manually.
Step 5: The calculator will display 406,573,821.
There are some typical errors that students might make during the process of cubing a number. Let us take a look at five of the major mistakes that students might make:
What is the cube and cube root of 741?
The cube of 741 is 406,573,821 and the cube root of 741 is approximately 8.984.
First, let’s find the cube of 741.
We know that 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 741³ = 406,573,821
Next, we must find the cube root of 741 We know that 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√741 ≈ 8.984
Hence the cube of 741 is 406,573,821 and the cube root of 741 is approximately 8.984.
If the side length of the cube is 741 cm, what is the volume?
The volume is 406,573,821 cm³.
Use the volume formula for a cube V = Side³.
Substitute 741 for the side length: V = 741³ = 406,573,821 cm³.
How much larger is 741³ than 700³?
741³ – 700³ = 63,573,821.
First, find the cube of 741, which is 406,573,821
Next, find the cube of 700, which is 343,000,000
Now, find the difference between them using the subtraction method. 406,573,821 – 343,000,000 = 63,573,821
Therefore, the 741³ is 63,573,821 larger than 700³.
If a cube with a side length of 741 cm is compared to a cube with a side length of 41 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 741 cm is 406,573,821 cm³.
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 741 means multiplying 741 by itself three times: 741 × 741 = 549,081, and then 549,081 × 741 = 406,573,821.
The unit of volume is cubic centimeters (cm³) because we are calculating the space inside the cube.
Therefore, the volume of the cube is 406,573,821 cm³.
Estimate the cube of 740 using the cube of 741.
The cube of 740 is approximately 406,573,821.
First, identify the cube of 741.
The cube of 741 is 741³ = 406,573,821.
Since 740 is only a tiny bit less than 741, the cube of 740 will be almost the same as the cube of 741.
The cube of 740 is approximately 406,573,821 because the difference between 740 and 741 is very small.
So, we can approximate the value as 406,573,821.
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.