100 LearnersLast updated on June 3rd, 2025
Cube of 685
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 685.
Cube of 685
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 685 can be written as 685³, which is the exponential form. Or it can also be written in arithmetic form as, 685 × 685 × 685.
How to Calculate the Value of Cube of 685
To check whether a number is a cube number or not, we can use the following three methods: multiplication method, a factor formula (a³), or by using a calculator. These three methods will help in cubing the numbers faster and easier without feeling confused or stuck while evaluating the answers.
- By Multiplication Method
- Using a Formula
- Using a Calculator
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. 685³ = 685 × 685 × 685
Step 2: You get 321,697,625 as the answer. Hence, the cube of 685 is 321,697,625.
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 685 into two parts. Let a = 600 and b = 85, so a + b = 685
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 600³ 3a²b = 3 × 600² × 85 3ab² = 3 × 600 × 85² b³ = 85³
Step 4: Add all the terms together:
(a + b)³ = a³ + 3a²b + 3ab² + b³
(600 + 85)³ = 600³ + 3 × 600² × 85 + 3 × 600 × 85² + 85³
685³ = 216,000,000 + 91,800,000 + 13,005,000 + 614,125
685³ = 321,697,625
Step 5: Hence, the cube of 685 is 321,697,625.
Using a Calculator
To find the cube of 685 using a calculator, input the number 685 and use the cube function (if available) or multiply 685 × 685 × 685. This operation calculates the value of 685³, resulting in 321,697,625. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 6 followed by 8 and 5
Step 3: If the calculator has a cube function, press it to calculate 685³.
Step 4: If there is no cube function on the calculator, simply multiply 685 three times manually.
Step 5: The calculator will display 321,697,625.
Tips and Tricks for the Cube of 685
- 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 685
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 that might be made:
Mistake 1
Incorrect Multiplication
One might multiply the numbers only twice. That is, 685 × 685 and not 685 × 685 × 685. Always remember that 685³ = 685 × 685 × 685.
Solved Examples on Cube of 685
Problem 1
What is the cube and cube root of 685?
The cube of 685 is 321,697,625 and the cube root of 685 is approximately 8.860.
Explanation
First, let’s find the cube of 685.
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 685³ = 321,697,625
Next, we must find the cube root of 685 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√685 ≈ 8.860
Hence the cube of 685 is 321,697,625 and the cube root of 685 is approximately 8.860.
Problem 2
If the side length of a cube is 685 cm, what is the volume?
The volume is 321,697,625 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 685 for the side length: V = 685³ = 321,697,625 cm³.
Problem 3
How much larger is 685³ than 600³?
685³ – 600³ = 105,697,625.
Explanation
First find the cube of 685, which is 321,697,625
Next, find the cube of 600, which is 216,000,000
Now, find the difference between them using the subtraction method. 321,697,625 – 216,000,000 = 105,697,625
Therefore, 685³ is 105,697,625 larger than 600³.
Problem 4
If a cube with a side length of 685 cm is compared to a cube with a side length of 100 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 685 cm is 321,697,625 cm³, and it is larger by 321,587,625 cm³ compared to the cube with a side length of 100 cm.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 685 means multiplying 685 by itself three times: 685 × 685 = 469,225, and then 469,225 × 685 = 321,697,625.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 321,697,625 cm³. For comparison, the volume of a cube with a side length of 100 cm is 100³ = 1,000,000 cm³.
So, the larger cube's volume is 321,697,625 cm³, which is 321,587,625 cm³ more than the smaller cube.
Problem 5
Estimate the cube of 684.9 using the cube of 685.
The cube of 684.9 is approximately 321,697,625.
Explanation
First, identify the cube of 685, The cube of 685 is 685³ = 321,697,625.
Since 684.9 is only a tiny bit less than 685, the cube of 684.9 will be almost the same as the cube of 685.
The cube of 684.9 is approximately 321,697,625 because the difference between 684.9 and 685 is very small.
So, we can approximate the value as 321,697,625.
FAQs on Cube of 685
1.What are the perfect cubes up to 685?
2.How do you calculate 685³?
3.What is the meaning of 685³?
4.What is the cube root of 685?
5.Is 685 a perfect cube?
6.How does learning Algebra help students in Oman make better decisions in daily life?
7.How can cultural or local activities in Oman support learning Algebra topics such as Cube of 685?
8.How do technology and digital tools in Oman support learning Algebra and Cube of 685?
9.Does learning Algebra support future career opportunities for students in Oman?
Important Glossaries for Cube of 685
- 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: Multiplying a number by itself three times is called the cube of a number.
- 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 equals 8.
- Perfect Cube: A number that can be expressed as the cube of an integer.
- Cube Root: A number that, when multiplied by itself three times, gives the original number.
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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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