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Last updated on May 27th, 2025

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Cube of 900

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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 the cube of 900.

Cube of 900 for Canadian Students
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Cube of 900

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 900 can be written as \(900^3\), which is the exponential form. Or it can also be written in arithmetic form as, \(900 \times 900 \times 900\).

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How to Calculate the Value of Cube of 900

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 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. \(900^3 = 900 \times 900 \times 900\) Step 2: Calculate the result to get 729,000,000 as the answer. Hence, the cube of 900 is 729,000,000.

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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 900 into two parts, as 800 and 100. Let \(a = 800\) and \(b = 100\), so \(a + b = 900\) Step 2: Now, apply the formula \((a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3\) Step 3: Calculate each term \(a^3 = 800^3\) \(3a^2b = 3 \times 800^2 \times 100\) \(3ab^2 = 3 \times 800 \times 100^2\) \(b^3 = 100^3\) Step 4: Add all the terms together: \((a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3\) \((800 + 100)^3 = 800^3 + 3 \times 800^2 \times 100 + 3 \times 800 \times 100^2 + 100^3\) \(900^3 = 512,000,000 + 192,000,000 + 24,000,000 + 1,000,000\) \(900^3 = 729,000,000\) Step 5: Hence, the cube of 900 is 729,000,000.

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Using a Calculator

To find the cube of 900 using a calculator, input the number 900 and use the cube function (if available) or multiply \(900 \times 900 \times 900\). This operation calculates the value of \(900^3\), resulting in 729,000,000. It’s a quick way to determine the cube without manual computation. Step 1: Ensure the calculator is functioning properly. Step 2: Press 9 followed by 0 and 0 Step 3: If the calculator has a cube function, press it to calculate \(900^3\). Step 4: If there is no cube function on the calculator, simply multiply 900 three times manually. Step 5: The calculator will display 729,000,000.

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Tips and Tricks for the Cube of 900

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 900

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, \(900 \times 900\) and not \(900 \times 900 \times 900\). Always remember that \(900^3 = 900 \times 900 \times 900\).

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Solved Examples on Cube of 900

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Problem 1

What is the cube and cube root of 900?

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The cube of 900 is 729,000,000, and the cube root of 900 is approximately 9.654.

Explanation

First, let’s find the cube of 900. We know that the cube of a number is such that \(x^3 = y\) Where \(x\) is the given number, and \(y\) is the cubed value of that number So, we get \(900^3 = 729,000,000\) Next, we must find the cube root of 900 We know that the cube root of a number \(x\) is such that \(\sqrt[3]{x} = y\) Where \(x\) is the given number, and \(y\) is the cube root value of the number So, we get \(\sqrt[3]{900} \approx 9.654\) Hence, the cube of 900 is 729,000,000 and the cube root of 900 is approximately 9.654.

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Problem 2

If the side length of the cube is 900 cm, what is the volume?

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The volume is 729,000,000 cm\(^3\).

Explanation

Use the volume formula for a cube \(V = \text{Side}^3\). Substitute 900 for the side length: \(V = 900^3 = 729,000,000\) cm\(^3\).

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Problem 3

How much larger is \(900^3\) than \(800^3\)?

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\(900^3 - 800^3 = 217,000,000\).

Explanation

First, find the cube of \(900^3\), which is 729,000,000 Next, find the cube of \(800^3\), which is 512,000,000 Now, find the difference between them using the subtraction method. 729,000,000 - 512,000,000 = 217,000,000 Therefore, the \(900^3\) is 217,000,000 larger than \(800^3\).

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Problem 4

If a cube with a side length of 900 cm is compared to a cube with a side length of 300 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 900 cm is 729,000,000 cm\(^3\).

Explanation

To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object). Cubing 900 means multiplying 900 by itself three times: \(900 \times 900 = 810,000\), and then \(810,000 \times 900 = 729,000,000\). The unit of volume is cubic centimeters (cm\(^3\)) because we are calculating the space inside the cube. Therefore, the volume of the cube is 729,000,000 cm\(^3\).

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Problem 5

Estimate the cube of 899 using the cube of 900.

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The cube of 899 is approximately 729,000,000.

Explanation

First, identify the cube of 900, The cube of 900 is \(900^3 = 729,000,000\). Since 899 is only a tiny bit less than 900, the cube of 899 will be almost the same as the cube of 900. The cube of 899 is approximately 729,000,000 because the difference between 899 and 900 is very small. So, we can approximate the value as 729,000,000.

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FAQs on Cube of 900

1.What are the perfect cubes up to 900?

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2.How do you calculate \(900^3\)?

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3.What is the meaning of \(900^3\)?

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4.What is the cube root of 900?

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5.Is 900 a perfect cube?

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

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7.How can cultural or local activities in Canada support learning Algebra topics such as Cube of 900?

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8.How do technology and digital tools in Canada support learning Algebra and Cube of 900?

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

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Important Glossaries for Cube of 900

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, \(2^3\) represents \(2 \times 2 \times 2\) equals 8. Perfect Cube: A number that can be expressed as the cube of an integer. Volume: The amount of space that a substance or object occupies or that is enclosed within a container, especially when great. For a cube, it is calculated as side length cubed.

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About BrightChamps in Canada

At BrightChamps, we understand algebra goes beyond digits—it opens doors to limitless possibilities! We aim to guide kids all across Canada to grasp key math skills, such as today’s focus on the Cube of 900, with a special emphasis on exploring cubes—in a fun, engaging, and easy-to-understand manner. Whether your child is measuring the speed of a roller coaster at Canada’s Wonderland, tracking hockey game scores, or budgeting their allowance for the latest gadgets, mastering algebra builds their everyday confidence. Our engaging lessons make learning both enjoyable and simple. Since Canadian children learn in various ways, we tailor our teaching to suit each learner’s style. From Toronto’s vibrant city life to the breathtaking views of British Columbia, BrightChamps makes algebra come alive, making it meaningful and exciting across Canada. Let’s make cubes a thrilling part of every child’s math story!
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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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