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 742.
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 742 can be written as 742³, which is the exponential form. Or it can also be written in arithmetic form as, 742 × 742 × 742.
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. 742³ = 742 × 742 × 742
Step 2: You get 408,046,088 as the answer. Hence, the cube of 742 is 408,046,088.
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 742 into two parts, as 700 and 42. Let a = 700 and b = 42, so a + b = 742
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term
a³ = 700³
3a²b = 3 × 700² × 42
3ab² = 3 × 700 × 42²
b³ = 42³
Step 4: Add all the terms together:
(a + b)³ = a³ + 3a²b + 3ab² + b³
(700 + 42)³ = 700³ + 3 × 700² × 42 + 3 × 700 × 42² + 42³
742³ = 343,000,000 + 61,740,000 + 37,044,000 + 74,088
742³ = 408,046,088
Step 5: Hence, the cube of 742 is 408,046,088.
To find the cube of 742 using a calculator, input the number 742 and use the cube function (if available) or multiply 742 × 742 × 742. This operation calculates the value of 742³, resulting in 408,046,088. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 7, 4, and 2
Step 3: If the calculator has a cube function, press it to calculate 742³.
Step 4: If there is no cube function on the calculator, simply multiply 742 three times manually.
Step 5: The calculator will display 408,046,088.
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 742?
The cube of 742 is 408,046,088 and the cube root of 742 is approximately 8.973.
First, let’s find the cube of 742.
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 742³ = 408,046,088
Next, we must find the cube root of 742 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√742 ≈ 8.973
Hence the cube of 742 is 408,046,088 and the cube root of 742 is approximately 8.973.
If the side length of the cube is 742 cm, what is the volume?
The volume is 408,046,088 cm³.
Use the volume formula for a cube V = Side³.
Substitute 742 for the side length: V = 742³ = 408,046,088 cm³.
How much larger is 742³ than 732³?
742³ – 732³ = 33,648,088.
First find the cube of 742³, that is 408,046,088
Next, find the cube of 732³, which is 374,398,000
Now, find the difference between them using the subtraction method. 408,046,088 – 374,398,000 = 33,648,088
Therefore, the 742³ is 33,648,088 larger than 732³.
If a cube with a side length of 742 cm is compared to a cube with a side length of 42 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 742 cm is 408,046,088 cm³
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 742 means multiplying 742 by itself three times: 742 × 742 = 550,564, and then 550,564 × 742 = 408,046,088.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 408,046,088 cm³.
Estimate the cube 741.9 using the cube 742.
The cube of 741.9 is approximately 408,046,088.
First, identify the cube of 742, The cube of 742 is 742³ = 408,046,088.
Since 741.9 is only a tiny bit less than 742, the cube of 741.9 will be almost the same as the cube of 742.
The cube of 741.9 is approximately 408,046,088 because the difference between 741.9 and 742 is very small.
So, we can approximate the value as 408,046,088.
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.