Cube of 742
2026-02-28 08:18 Diff
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Last updated on August 5, 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.

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.

How to Calculate the Value of Cube of 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.

  1. By Multiplication Method
  2. Using a Formula
  3. Using a Calculator

By Multiplication Method

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.

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Using a Formula (a³)

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.

Using a Calculator

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.

Tips and Tricks for the Cube of 742

  • The product of two or more perfect cube numbers is always a perfect cube.
  • A perfect cube can always be expressed as the product of three identical groups of equal prime factors.

Common Mistakes to Avoid When Calculating the Cube of 742

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:

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Problem 1

What is the cube and cube root of 742?

Okay, lets begin

The cube of 742 is 408,046,088 and the cube root of 742 is approximately 8.973.

Explanation

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.

Well explained 👍

Problem 2

If the side length of the cube is 742 cm, what is the volume?

Okay, lets begin

The volume is 408,046,088 cm³.

Explanation

Use the volume formula for a cube V = Side³.

Substitute 742 for the side length: V = 742³ = 408,046,088 cm³.

Well explained 👍

Problem 3

How much larger is 742³ than 732³?

Okay, lets begin

742³ – 732³ = 33,648,088.

Explanation

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.

Well explained 👍

Problem 4

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?

Okay, lets begin

The volume of the cube with a side length of 742 cm is 408,046,088 cm³

Explanation

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.

Well explained 👍

Problem 5

Estimate the cube 741.9 using the cube 742.

Okay, lets begin

The cube of 741.9 is approximately 408,046,088.

Explanation

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.

Well explained 👍

FAQs on Cube of 742

1.What are the perfect cubes up to 742?

The perfect cubes up to 742 are 1, 8, 27, 64, 125, 216, 343, 512, and 729.

2.How do you calculate 742³?

To calculate 742³, use the multiplication method, 742 × 742 × 742, which equals 408,046,088.

3.What is the meaning of 742³?

742³ means 742 multiplied by itself three times, or 742 × 742 × 742.

4.What is the cube root of 742?

5.Is 742 a perfect cube?

No, 742 is not a perfect cube because no integer multiplied by itself three times equals 742.

Important Glossaries for Cube of 742

  • Binomial Formula: It is an algebraic expression used to expand the powers of a number, written as (a + b)ⁿ, where ‘n’ is a positive integer raised to the base. The formula is used to find the square and cube of a number.
  • Cube of a Number: Multiplying a number by itself three times is called the cube of a number.
  • Exponential Form: It is a way of expressing numbers using a base and an exponent (or power), where the exponent value indicates how many times the base is multiplied by itself. For example, 2³ represents 2 × 2 × 2, which equals 8.
  • Perfect Cube: A number that can be expressed as the cube of an integer. For example, 8 is a perfect cube because it can be written as 2³.
  • Volume of a Cube: The amount of space enclosed within a cube, calculated as the cube of the side length. For example, for a cube with side length s, the volume is s³.

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Jaskaran Singh Saluja

About the Author

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.

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.