Cube of 324
2026-02-28 01:35 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 324.

Cube of 324

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 by itself three times results in a negative number.

The cube of 324 can be written as 324³, which is the exponential form. Or it can also be written in arithmetic form as 324 × 324 × 324.

How to Calculate the Value of Cube of 324

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 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. 324³ = 324 × 324 × 324

Step 2: You get 34,012,224 as the answer. Hence, the cube of 324 is 34,012,224.

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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 324 into two parts. Let a = 320 and b = 4, so a + b = 324

Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³

Step 3: Calculate each term

a³ = 320³

3a²b = 3 × 320² × 4

3ab² = 3 × 320 × 4²

b³ = 4³

Step 4: Add all the terms together:

(a + b)³ = a³ + 3a²b + 3ab² + b³

(320 + 4)³ = 320³ + 3 × 320² × 4 + 3 × 320 × 4² + 4³

324³ = 32,768,000 + 1,228,800 + 15,360 + 64

324³ = 34,012,224

Step 5: Hence, the cube of 324 is 34,012,224.

Using a Calculator

To find the cube of 324 using a calculator, input the number 324 and use the cube function (if available) or multiply 324 × 324 × 324. This operation calculates the value of 324³, resulting in 34,012,224. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Press 3 followed by 2 and 4

Step 3: If the calculator has a cube function, press it to calculate 324³.

Step 4: If there is no cube function on the calculator, simply multiply 324 three times manually.

Step 5: The calculator will display 34,012,224.

Tips and Tricks for the Cube of 324

  • 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 324

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 324?

Okay, lets begin

The cube of 324 is 34,012,224 and the cube root of 324 is approximately 6.903.

Explanation

First, let’s find the cube of 324.

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 324³ = 34,012,224.

Next, we must find the cube root of 324.

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√324 ≈ 6.903.

Hence, the cube of 324 is 34,012,224 and the cube root of 324 is approximately 6.903.

Well explained 👍

Problem 2

If the side length of the cube is 324 cm, what is the volume?

Okay, lets begin

The volume is 34,012,224 cm³.

Explanation

Use the volume formula for a cube V = Side³.

Substitute 324 for the side length: V = 324³ = 34,012,224 cm³.

Well explained 👍

Problem 3

How much larger is 324³ than 320³?

Okay, lets begin

324³ – 320³ = 1,244,224.

Explanation

First find the cube of 324³, which is 34,012,224. Next, find the cube of 320³, which is 32,768,000.

Now, find the difference between them using the subtraction method.

34,012,224 – 32,768,000 = 1,244,224.

Therefore, 324³ is 1,244,224 larger than 320³.

Well explained 👍

Problem 4

If a cube with a side length of 324 cm is compared to a cube with a side length of 4 cm, how much larger is the volume of the larger cube?

Okay, lets begin

The volume of the cube with a side length of 324 cm is 34,012,224 cm³.

Explanation

To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).

Cubing 324 means multiplying 324 by itself three times: 324 × 324 = 104,976, and then 104,976 × 324 = 34,012,224.

The unit of volume is cubic centimeters (cm³) because we are calculating the space inside the cube.

Therefore, the volume of the cube is 34,012,224 cm³.

Well explained 👍

Problem 5

Estimate the cube 323.9 using the cube 324.

Okay, lets begin

The cube of 323.9 is approximately 34,012,224.

Explanation

First, identify the cube of 324, The cube of 324 is 324³ = 34,012,224.

Since 323.9 is only a tiny bit less than 324, the cube of 323.9 will be almost the same as the cube of 324.

The cube of 323.9 is approximately 34,012,224 because the difference between 323.9 and 324 is very small.

So, we can approximate the value as 34,012,224.

Well explained 👍

FAQs on Cube of 324

1.What are the perfect cubes up to 324?

The perfect cubes up to 324 include 1, 8, 27, 64, 125, 216.

2.How do you calculate 324³?

To calculate 324³, use the multiplication method, 324 × 324 × 324, which equals 34,012,224.

3.What is the meaning of 324³?

324³ means 324 multiplied by itself three times, or 324 × 324 × 324.

4.What is the cube root of 324?

5.Is 324 a perfect cube?

No, 324 is not a perfect cube because no integer multiplied by itself three times equals 324.

Important Glossaries for Cube of 324

  • 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, 3³ represents 3 × 3 × 3, which equals 27.
  • Cube Root: The cube root of a number is a value that, when multiplied by itself twice, gives the original number. It is denoted as ³√x.
  • Volume of a Cube: The amount of space inside the cube, calculated as the side length raised to the power of three (Side³).

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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.