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Last updated on June 1st, 2025

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Cube of 564

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When a number is multiplied by itself thrice, the resultant number is called the cube of a number. Cubing is used in comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of 564.

Cube of 564 for Indian Students
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Cube of 564

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 564 can be written as 564³, which is the exponential form.

 

Or it can also be written in arithmetic form as, 564 × 564 × 564.

cube of 564

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How to Calculate the Value of Cube of 564

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 you to cube the numbers faster and easier without feeling confused or stuck while evaluating the answers.

 

  • By Multiplication Method
     
  • Using a Formula
     
  • Using a Calculator
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By Multiplication Method

The multiplication method is a process in mathematics used to find the product of 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. 564³ = 564 × 564 × 564

 

Step 2: You get 179,992,704 as the answer. Hence, the cube of 564 is 179,992,704.

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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 564 into two parts. Let a = 500 and b = 64, so a + b = 564

 

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

 

Step 3: Calculate each term a³ = 500³ 3a²b = 3 × 500² × 64 3ab² = 3 × 500 × 64² b³ = 64³

 

Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (500 + 64)³ = 500³ + 3 × 500² × 64 + 3 × 500 × 64² + 64³ 564³ = 125,000,000 + 48,000,000 + 6,144,000 + 262,144 564³ = 179,992,704

 

Step 5: Hence, the cube of 564 is 179,992,704.

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Using a Calculator

To find the cube of 564 using a calculator, input the number 564 and use the cube function (if available) or multiply 564 × 564 × 564. This operation calculates the value of 564³, resulting in 179,992,704. It’s a quick way to determine the cube without manual computation.

 

Step 1: Ensure the calculator is functioning properly.

 

Step 2: Input 564 Step 3: If the calculator has a cube function, press it to calculate 564³.

 

Step 4: If there is no cube function on the calculator, simply multiply 564 three times manually.

 

Step 5: The calculator will display 179,992,704.

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Tips and Tricks for the Cube of 564

  • The cube of any even number is always even, while the cube of any odd number is always odd.
     
  • 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.
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Common Mistakes to Avoid When Calculating the Cube of 564

There are some typical errors that might occur during the process of cubing a number. Let us take a look at five of the major mistakes:

Mistake 1

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Incorrect Multiplication

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One might multiply the numbers only twice. That is, 564 × 564 and not 564 × 564 × 564. Always remember that 564³ = 564 × 564 × 564.

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Solved Examples on Cube of 564

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Problem 1

What is the cube and cube root of 564?

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The cube of 564 is 179,992,704 and the cube root of 564 is approximately 8.24.

Explanation

First, let’s find the cube of 564.

We know that the cube of a number, x³ = y

Where x is the given number, and y is the cubed value of that number.

So, we get 564³ = 179,992,704 Next, we must find the cube root of 564.

We know that the cube root of a number 'x', such that ∛x = y

Where 'x' is the given number, and y is the cube root value of the number.

So, we get ∛564 ≈ 8.24 Hence, the cube of 564 is 179,992,704 and the cube root of 564 is approximately 8.24.

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Problem 2

If the side length of the cube is 564 cm, what is the volume?

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The volume is 179,992,704 cm³.

Explanation

Use the volume formula for a cube V = Side³.

Substitute 564 for the side length: V = 564³ = 179,992,704 cm³.

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Problem 3

How much larger is 564³ than 464³?

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564³ – 464³ = 110,224,704.

Explanation

First find the cube of 564, that is 179,992,704

Next, find the cube of 464, which is 69,768,000

Now, find the difference between them using the subtraction method. 179,992,704 – 69,768,000 = 110,224,704

Therefore, 564³ is 110,224,704 larger than 464³.

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Problem 4

If a cube with a side length of 564 cm is compared to a cube with a side length of 100 cm, how much larger is the volume of the larger cube?

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The volume of the cube with a side length of 564 cm is 179,992,704 cm³.

Explanation

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

Cubing 564 means multiplying 564 by itself three times: 564 × 564 = 318,096, and then 318,096 × 564 = 179,992,704.

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

Therefore, the volume of the cube is 179,992,704 cm³.

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Problem 5

Estimate the cube 563.9 using the cube 564.

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The cube of 563.9 is approximately 179,992,704.

Explanation

First, identify the cube of 564,

The cube of 564 is 564³ = 179,992,704.

Since 563.9 is only a tiny bit less than 564, the cube of 563.9 will be almost the same as the cube of 564.

The cube of 563.9 is approximately 179,992,704 because the difference between 563.9 and 564 is very small.

So, we can approximate the value as 179,992,704.

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FAQs on Cube of 564

1.What are the perfect cubes up to 564?

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2.How do you calculate 564³?

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3.What is the meaning of 564³?

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4.What is the cube root of 564?

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5.Is 564 a perfect cube?

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6.How does learning Algebra help students in India make better decisions in daily life?

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7.How can cultural or local activities in India support learning Algebra topics such as Cube of 564?

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8.How do technology and digital tools in India support learning Algebra and Cube of 564?

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9.Does learning Algebra support future career opportunities for students in India?

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Important Glossaries for Cube of 564

  • Binomial Formula: 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: The result of multiplying a number by itself three times.
     
  • Exponential Form: 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.
     
  • Volume of a Cube: The amount of space occupied by a cube, calculated by raising the length of one side to the third power.
     
  • Perfect Cube: A number that can be expressed as the product of an integer multiplied by itself twice more (i.e., cubed).
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About BrightChamps in India

At BrightChamps, algebra is more than just calculations—it’s a key to endless opportunities! We’re dedicated to helping kids throughout India learn essential math skills, focusing today on the Cube of 564, with an engaging emphasis on understanding cubes—in a way that’s clear, lively, and fun. Whether your child is working out how fast a train passes by, following scores during a cricket match, or managing their pocket money to buy new gadgets, mastering algebra equips them with the confidence needed for daily life. Our interactive classes make learning easy and enjoyable. Since children in India learn in different ways, we customize our approach to fit each child’s unique learning style. From the busy markets of Mumbai to Delhi’s vibrant streets, BrightChamps makes algebra relatable and exciting all across India. Let’s make cubes a delightful part of every child’s math journey!
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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.

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Fun Fact

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

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