115 LearnersLast updated on May 29th, 2025
Cube of 86
When a number is multiplied by itself thrice, the resultant number is called the cube of a number. Cubing is used when comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of 86.
Cube of 86
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 86 can be written as 863, which is the exponential form.
Or it can also be written in arithmetic form as 86 × 86 × 86.
How to Calculate the Value of Cube of 86
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 (a^3), 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 (a3)
- 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. 863 = 86 × 86 × 86
Step 2: You get 636,056 as the answer.
Hence, the cube of 86 is 636,056.
Using a Formula (a^3)
The formula (a + b)^3 is a binomial formula for finding the cube of a number. The formula is expanded as a^3 + 3a^2b + 3ab^2 + b^3.
Step 1: Split the number 86 into two parts, as 80 and 6. Let a = 80 and b = 6, so a + b = 86
Step 2: Now, apply the formula (a + b)3 = a3 + 3a2b + 3ab2 + b3
Step 3: Calculate each term a3 = 803 3a2b = 3 × 802 × 6 3ab2 = 3 × 80 × 62 b3 = 63
Step 4: Add all the terms together: (a + b)3 = a3 + 3a2b + 3ab2 + b3 (80 + 6)3 = 803 + 3 × 802 × 6 + 3 × 80 × 62 + 63 863 = 512000 + 115200 + 8640 + 216 863 = 636056
Step 5: Hence, the cube of 86 is 636,056.
Using a Calculator
To find the cube of 86 using a calculator, input the number 86 and use the cube function (if available) or multiply 86 × 86 × 86. This operation calculates the value of 863, resulting in 636,056. 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
Step 3: If the calculator has a cube function, press it to calculate 863.
Step 4: If there is no cube function on the calculator, simply multiply 86 three times manually.
Step 5: The calculator will display 636,056.
Tips and Tricks for the Cube of 86
- 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.
Common Mistakes to Avoid When Calculating the Cube of 86
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
Incorrect Multiplication
Kids might multiply the numbers only twice. That is, 86 × 86 and not 86 × 86 × 86. Always remember that 863 = 86 × 86 × 86.
Solved Examples on Cube of 86
Problem 1
What is the cube and cube root of 86?
The cube of 86 is 636,056 and the cube root of 86 is approximately 4.430.
Explanation
First, let’s find the cube of 86.
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 863 = 636,056 Next, we must find the cube root of 86
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√86 ≈ 4.430 Hence the cube of 86 is 636,056 and the cube root of 86 is approximately 4.430.
Problem 2
If the side length of the cube is 86 cm, what is the volume?
The volume is 636,056 cm³.
Explanation
Use the volume formula for a cube V = Side3.
Substitute 86 for the side length: V = 863 = 636,056 cm³.
Problem 3
How much larger is 86^3 than 76^3?
86^3 – 76^3 = 286,776.
Explanation
First find the cube of 863, that is 636,056
Next, find the cube of 763, which is 349,280
Now, find the difference between them using the subtraction method. 636,056 – 349,280 = 286,776
Therefore, 863 is 286,776 larger than 763.
Problem 4
If a cube with a side length of 86 cm is compared to a cube with a side length of 16 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 86 cm is 636,056 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 86 means multiplying 86 by itself three times: 86 × 86 = 7,396, and then 7,396 × 86 = 636,056.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 636,056 cm³.
Problem 5
Estimate the cube of 85.9 using the cube of 86.
The cube of 85.9 is approximately 636,056.
Explanation
First, identify the cube of 86,
The cube of 86 is 863 = 636,056.
Since 85.9 is only a tiny bit less than 86, the cube of 85.9 will be almost the same as the cube of 86.
The cube of 85.9 is approximately 636,056 because the difference between 85.9 and 86 is very small.
So, we can approximate the value as 636,056.
FAQs on Cube of 86
1.What are the perfect cubes up to 86?
2.How do you calculate 86^3?
3.What is the meaning of 86^3?
4.What is the cube root of 86?
5.Is 86 a perfect cube?
6.How does learning Algebra help students in Australia make better decisions in daily life?
7.How can cultural or local activities in Australia support learning Algebra topics such as Cube of 86?
8.How do technology and digital tools in Australia support learning Algebra and Cube of 86?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for Cube of 86
- 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.
- Volume of a Cube: The space occupied by a cube, calculated as the side length raised to the power of 3 (Side3).
- Perfect Cube: A number that can be expressed as the cube of an integer. Examples include 1, 8, and 27.
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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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