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Last updated on June 1st, 2025

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Cube of 396

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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 while comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about cubes of 396.

Cube of 396 for Bahraini Students
Professor Greenline from BrightChamps

Cube of 396

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 396 can be written as 396³, which is the exponential form.

 

Or it can also be written in arithmetic form as 396 × 396 × 396.

cube of 396

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How to Calculate the Value of Cube of 396

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 kids 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 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. 396³ = 396 × 396 × 396

 

Step 2: You get 62,035,776 as the answer. Hence, the cube of 396 is 62,035,776.

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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 396 into two parts, as and . Let a = 400 and b = -4, so a + b = 396

 

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

 

Step 3: Calculate each term a³ = 400³ 3a²b = 3 × 400² × (-4) 3ab² = 3 × 400 × (-4)² b³ = (-4)³

 

Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (400 - 4)³ = 400³ + 3 × 400² × (-4) + 3 × 400 × 16 + (-64) 396³ = 64,000,000 - 1,920,000 + 19,200 - 64 396³ = 62,035,776

 

Step 5: Hence, the cube of 396 is 62,035,776.

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Using a Calculator

To find the cube of 396 using a calculator, input the number 396 and use the cube function (if available) or multiply 396 × 396 × 396. This operation calculates the value of 396³, resulting in 62,035,776. 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 9 and then 6

 

Step 3: If the calculator has a cube function, press it to calculate 396³.

 

Step 4: If there is no cube function on the calculator, simply multiply 396 three times manually.

 

Step 5: The calculator will display 62,035,776.

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Tips and Tricks for the Cube of 396

  • 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 396

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:

Mistake 1

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Incorrect Multiplication

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Kids might multiply the numbers only twice. That is, 396 × 396 and not 396 × 396 × 396. Always remember that 396³ = 396 × 396 × 396.

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Solved Examples on Cube of 396

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Problem 1

What is the cube and cube root of 396?

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The cube of 396 is 62,035,776 and the cube root of 396 is approximately 7.368.

Explanation

First, let’s find the cube of 396.

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 396³ = 62,035,776

Next, we must find the cube root of 396 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 ∛396 ≈ 7.368

Hence the cube of 396 is 62,035,776 and the cube root of 396 is approximately 7.368.

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Problem 2

If the side length of a cube is 396 cm, what is the volume?

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The volume is 62,035,776 cm³.

Explanation

Use the volume formula for a cube V = Side³.

Substitute 396 for the side length: V = 396³ = 62,035,776 cm³.

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Problem 3

How much larger is 396³ than 200³?

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396³ – 200³ = 61,835,776.

Explanation

First, find the cube of 396, that is 62,035,776.

Next, find the cube of 200, which is 8,000,000.

Now, find the difference between them using the subtraction method. 62,035,776 – 8,000,000 = 61,835,776.

Therefore, 396³ is 61,835,776 larger than 200³.

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Problem 4

If a cube with a side length of 396 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 396 cm is 62,035,776 cm³.

Explanation

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

Cubing 396 means multiplying 396 by itself three times: 396 × 396 = 156,816, and then 156,816 × 396 = 62,035,776.

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

Therefore, the volume of the cube is 62,035,776 cm³.

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Problem 5

Estimate the cube of 395.5 using the cube of 396.

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The cube of 395.5 is approximately 62,035,776.

Explanation

First, identify the cube of 396,

The cube of 396 is 396³ = 62,035,776.

Since 395.5 is only a tiny bit less than 396, the cube of 395.5 will be almost the same as the cube of 396.

The cube of 395.5 is approximately 62,035,776 because the difference between 395.5 and 396 is very small.

So, we can approximate the value as 62,035,776.

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FAQs on Cube of 396

1.What are the perfect cubes up to 396?

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2.How do you calculate 396³?

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3.What is the meaning of 396³?

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4.What is the cube root of 396?

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5.Is 396 a perfect cube?

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

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7.How can cultural or local activities in Bahrain support learning Algebra topics such as Cube of 396?

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8.How do technology and digital tools in Bahrain support learning Algebra and Cube of 396?

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

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Professor Greenline from BrightChamps

Important Glossaries for Cube of 396

  • 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 equals 8.
     
  • Perfect Cube: A number that can be expressed as the product of an integer multiplied by itself twice more. For example, 8 is a perfect cube because it is 2 × 2 × 2.
     
  • Volume: The amount of space occupied by a 3-dimensional object, like a cube, measured in cubic units.
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About BrightChamps in Bahrain

At BrightChamps, algebra is more than just digits—it unlocks endless opportunities! We strive to help kids all across Bahrain develop key math skills, focusing today on the Cube of 396 with an exciting look at cubes—in a lively, clear, and enjoyable way. Whether your child is figuring out the speed of a roller coaster at Bahrain’s Wahooo! Waterpark, tracking football scores, or managing their allowance for the latest gadgets, mastering algebra gives them confidence in everyday challenges. Our interactive lessons make math easy and fun. Because kids in Bahrain learn differently, we tailor our teaching to each child’s learning style. From Manama’s lively city life to Bahrain’s peaceful beaches, BrightChamps makes algebra come alive, making it exciting and relevant across Bahrain. Let’s make cubes a fun 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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