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 often used when comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of 743.
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 743 can be written as 743³, which is the exponential form. Or it can also be written in arithmetic form as 743 × 743 × 743.
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 students to cube 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. 743³ = 743 × 743 × 743
Step 2: You get 409,607,047 as the answer. Hence, the cube of 743 is 409,607,047.
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 743 into two parts, such as 700 and 43. Let a = 700 and b = 43, so a + b = 743
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term
a³ = 700³
3a²b = 3 × 700² × 43
3ab² = 3 × 700 × 43²
b³ = 43³
Step 4: Add all the terms together:
(a + b)³ = a³ + 3a²b + 3ab² + b³
(700 + 43)³ = 700³ + 3 × 700² × 43 + 3 × 700 × 43² + 43³
743³ = 343,000,000 + 63,210,000 + 38,949 + 79,507
743³ = 409,607,047
Step 5: Hence, the cube of 743 is 409,607,047.
To find the cube of 743 using a calculator, input the number 743 and use the cube function (if available) or multiply 743 × 743 × 743. This operation calculates the value of 743³, resulting in 409,607,047. 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, and 3.
Step 3: If the calculator has a cube function, press it to calculate 743³.
Step 4: If there is no cube function on the calculator, simply multiply 743 three times manually.
Step 5: The calculator will display 409,607,047.
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 they might make:
What is the cube and cube root of 743?
The cube of 743 is 409,607,047 and the cube root of 743 is approximately 8.988.
First, let’s find the cube of 743.
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 743³ = 409,607,047.
Next, we must find the cube root of 743. The cube root of a number ‘x’ is such that ∛x = y, where ‘x’ is the given number, and y is the cube root value of the number.
So, we get ∛743 ≈ 8.988.
Hence the cube of 743 is 409,607,047 and the cube root of 743 is approximately 8.988.
If the side length of the cube is 743 cm, what is the volume?
The volume is 409,607,047 cm³.
Use the volume formula for a cube V = Side³.
Substitute 743 for the side length: V = 743³ = 409,607,047 cm³.
How much larger is 743³ than 700³?
743³ – 700³ = 66,607,047.
First, find the cube of 743, which is 409,607,047.
Next, find the cube of 700, which is 343,000,000.
Now, find the difference between them using the subtraction method.
409,607,047 – 343,000,000 = 66,607,047.
Therefore, 743³ is 66,607,047 larger than 700³.
If a cube with a side length of 743 cm is compared to a cube with a side length of 43 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 743 cm is 409,607,047 cm³.
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 743 means multiplying 743 by itself three times: 743 × 743 = 552,049, and then 552,049 × 743 = 409,607,047.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 409,607,047 cm³.
Estimate the cube of 742.9 using the cube of 743.
The cube of 742.9 is approximately 409,607,047.
First, identify the cube of 743.
The cube of 743 is 743³ = 409,607,047. Since 742.9 is only a tiny bit less than 743, the cube of 742.9 will be almost the same as the cube of 743.
The cube of 742.9 is approximately 409,607,047 because the difference between 742.9 and 743 is very small.
So, we can approximate the value as 409,607,047.
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.