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Last updated on May 27th, 2025

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Cube of 867

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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 867.

Cube of 867 for UK Students
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Cube of 867

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 867 can be written as 867³, which is the exponential form. Or it can also be written in arithmetic form as, 867 × 867 × 867.

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How to Calculate the Value of Cube of 867

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. 867³ = 867 × 867 × 867 Step 2: You get 651,423,963 as the answer. Hence, the cube of 867 is 651,423,963.

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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 867 into two parts, as 800 and 67. Let a = 800 and b = 67, so a + b = 867 Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³ Step 3: Calculate each term a³ = 800³ 3a²b = 3 × 800² × 67 3ab² = 3 × 800 × 67² b³ = 67³ Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (800 + 67)³ = 800³ + 3 × 800² × 67 + 3 × 800 × 67² + 67³ 867³ = 512,000,000 + 128,160,000 + 10,795,200 + 300,763 867³ = 651,423,963 Step 5: Hence, the cube of 867 is 651,423,963.

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Using a Calculator

To find the cube of 867 using a calculator, input the number 867 and use the cube function (if available) or multiply 867 × 867 × 867. This operation calculates the value of 867³, resulting in 651,423,963. It’s a quick way to determine the cube without manual computation. Step 1: Ensure the calculator is functioning properly. Step 2: Press 8 followed by 6 and 7 Step 3: If the calculator has a cube function, press it to calculate 867³. Step 4: If there is no cube function on the calculator, simply multiply 867 three times manually. Step 5: The calculator will display 651,423,963.

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Tips and Tricks for the Cube of 867

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 867

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, 867 × 867 and not 867 × 867 × 867. Always remember that 867³ = 867 × 867 × 867.

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Solved Examples on Cube of 867

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Problem 1

What is the cube and cube root of 867?

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The cube of 867 is 651,423,963 and the cube root of 867 is approximately 9.545.

Explanation

First, let’s find the cube of 867. We know that 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 867³ = 651,423,963 Next, we must find the cube root of 867 We know that 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 ∛867 ≈ 9.545 Hence the cube of 867 is 651,423,963 and the cube root of 867 is approximately 9.545.

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Problem 2

If the side length of the cube is 867 cm, what is the volume?

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The volume is 651,423,963 cm³.

Explanation

Use the volume formula for a cube V = Side³. Substitute 867 for the side length: V = 867³ = 651,423,963 cm³.

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Problem 3

How much larger is 867³ than 800³?

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867³ – 800³ = 139,423,963.

Explanation

First find the cube of 867, that is 651,423,963. Next, find the cube of 800, which is 512,000,000. Now, find the difference between them using the subtraction method. 651,423,963 – 512,000,000 = 139,423,963 Therefore, 867³ is 139,423,963 larger than 800³.

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Problem 4

If a cube with a side length of 867 cm is compared to a cube with a side length of 67 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 867 cm is 651,423,963 cm³.

Explanation

To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object). Cubing 867 means multiplying 867 by itself three times: 867 × 867 = 751,689, and then 751,689 × 867 = 651,423,963. The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube. Therefore, the volume of the cube is 651,423,963 cm³.

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Problem 5

Estimate the cube 866.9 using the cube 867.

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The cube of 866.9 is approximately 651,423,963.

Explanation

First, identify the cube of 867, The cube of 867 is 867³ = 651,423,963. Since 866.9 is only a tiny bit less than 867, the cube of 866.9 will be almost the same as the cube of 867. The cube of 866.9 is approximately 651,423,963 because the difference between 866.9 and 867 is very small. So, we can approximate the value as 651,423,963.

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FAQs on Cube of 867

1.What are the perfect cubes up to 867?

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2.How do you calculate 867³?

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3.What is the meaning of 867³?

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4.What is the cube root of 867?

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5.Is 867 a perfect cube?

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

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7.How can cultural or local activities in United Kingdom support learning Algebra topics such as Cube of 867?

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8.How do technology and digital tools in United Kingdom support learning Algebra and Cube of 867?

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

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Important Glossaries for Cube of 867

Binomial Formula: It is an algebraic expression used to expand the powers of a number, written as (a + b)³, where ‘n’ is a positive integer raised to the base. The formula is used to find the 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. Cube Root: The number that, when multiplied by itself three times, gives the original number. For instance, the cube root of 27 is 3. Volume of a Cube: The space occupied by a cube, calculated by cubing the side length, expressed as Side³.

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About BrightChamps in United Kingdom

At BrightChamps, we know algebra is more than just figures—it’s a doorway to endless opportunities! Our mission is to help children across the United Kingdom grasp vital math skills, like today’s spotlight on the Cube of 867, with an exciting focus on understanding cubes—in a lively, straightforward, and enjoyable way. Whether your child is figuring out the speed of a roller coaster at Alton Towers, keeping score at a local football match, or managing pocket money for the latest gadgets, mastering algebra gives them the confidence to face everyday challenges. Our interactive sessions keep learning fun and simple. Because children in the UK have different ways of learning, we adapt our approach to fit their unique styles. From London’s busy streets to the scenic Cornwall coast, BrightChamps makes algebra relatable and thrilling throughout the UK. Let’s turn cubes into a fun part of every child’s math adventure!
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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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