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Last updated on May 27th, 2025

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Cube of 850

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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 when comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about cubes of 850.

Cube of 850 for Thai Students
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Cube of 850

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 850 can be written as 850³, which is the exponential form. Or it can also be written in arithmetic form as, 850 × 850 × 850.

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How to Calculate the Value of Cube of 850

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. 850³ = 850 × 850 × 850 Step 2: You get 614,125,000 as the answer. Hence, the cube of 850 is 614,125,000.

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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 850 into two parts, as 800 and 50. Let a = 800 and b = 50, so a + b = 850 Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³ Step 3: Calculate each term a³ = 800³ 3a²b = 3 × 800² × 50 3ab² = 3 × 800 × 50² b³ = 50³ Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (800 + 50)³ = 800³ + 3 × 800² × 50 + 3 × 800 × 50² + 50³ 850³ = 512,000,000 + 96,000,000 + 60,000,000 + 125,000 850³ = 614,125,000 Step 5: Hence, the cube of 850 is 614,125,000.

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Using a Calculator

To find the cube of 850 using a calculator, input the number 850 and use the cube function (if available) or multiply 850 × 850 × 850. This operation calculates the value of 850³, resulting in 614,125,000. 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 5 and 0 Step 3: If the calculator has a cube function, press it to calculate 850³. Step 4: If there is no cube function on the calculator, simply multiply 850 three times manually. Step 5: The calculator will display 614,125,000.

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Tips and Tricks for the Cube of 850

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 850

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, 850 × 850 and not 850 × 850 × 850. Always remember that 850³ = 850 × 850 × 850.

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Solved Examples on Cube of 850

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Problem 1

What is the cube and cube root of 850?

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The cube of 850 is 614,125,000 and the cube root of 850 is approximately 9.448.

Explanation

First, let’s find the cube of 850. 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 850³ = 614,125,000 Next, we must find the cube root of 850 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 ∛850 ≈ 9.448 Hence, the cube of 850 is 614,125,000 and the cube root of 850 is approximately 9.448.

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Problem 2

If the side length of the cube is 850 cm, what is the volume?

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The volume is 614,125,000 cm³.

Explanation

Use the volume formula for a cube V = Side³. Substitute 850 for the side length: V = 850³ = 614,125,000 cm³.

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Problem 3

How much larger is 850³ than 800³?

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850³ – 800³ = 102,125,000

Explanation

First, find the cube of 850³, that is 614,125,000 Next, find the cube of 800³, which is 512,000,000 Now, find the difference between them using the subtraction method. 614,125,000 – 512,000,000 = 102,125,000 Therefore, the 850³ is 102,125,000 larger than 800³.

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Problem 4

If a cube with a side length of 850 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 850 cm is 614,125,000 cm³

Explanation

To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object). Cubing 850 means multiplying 850 by itself three times: 850 × 850 = 722,500, and then 722,500 × 850 = 614,125,000. The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube. Therefore, the volume of the cube is 614,125,000 cm³.

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Problem 5

Estimate the cube 849 using the cube 850.

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The cube of 849 is approximately 614,125,000.

Explanation

First, identify the cube of 850, The cube of 850 is 850³ = 614,125,000. Since 849 is only a tiny bit less than 850, the cube of 849 will be almost the same as the cube of 850. The cube of 849 is approximately 614,125,000 because the difference between 849 and 850 is very small. So, we can approximate the value as 614,125,000.

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FAQs on Cube of 850

1.What are the perfect cubes up to 850?

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2.How do you calculate 850³?

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3.What is the meaning of 850³?

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4.What is the cube root of 850?

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5.Is 850 a perfect cube?

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

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7.How can cultural or local activities in Thailand support learning Algebra topics such as Cube of 850?

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8.How do technology and digital tools in Thailand support learning Algebra and Cube of 850?

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

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Important Glossaries for Cube of 850

1. 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. 2. Cube of a Number: Multiplying a number by itself three times is called the cube of a number. 3. 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. 4. Perfect Cube: A number that can be expressed as the cube of an integer. 5. Volume of a Cube: The amount of space a cube occupies, calculated as the cube of its side length.

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About BrightChamps in Thailand

At BrightChamps, algebra goes beyond just numbers—it’s the key to countless opportunities! We strive to help children across Thailand master important math skills, like today’s focus on the Cube of 850, with an exciting look at cubes—in a lively, easy-to-understand, and fun way. Whether your child is calculating how fast a roller coaster moves at Dream World, tracking scores at a local football game, or managing their allowance for the newest gadgets, knowing algebra builds the confidence they need every day. Our interactive lessons keep math fun and simple. Because children in Thailand learn in diverse ways, we adapt our teaching to fit each child’s unique style. From bustling Bangkok streets to Phuket’s tropical islands, BrightChamps makes algebra relatable and exciting throughout Thailand. Let’s make cubes a joyful 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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