Last updated on May 27th, 2025
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.
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, \(900 \times 900 \times 900\).
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
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.
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.
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.
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.
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:
What is the cube and cube root of 900?
The cube of 900 is 729,000,000, and the cube root of 900 is approximately 9.654.
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.
If the side length of the cube is 900 cm, what is the volume?
The volume is 729,000,000 cm\(^3\).
Use the volume formula for a cube \(V = \text{Side}^3\). Substitute 900 for the side length: \(V = 900^3 = 729,000,000\) cm\(^3\).
How much larger is \(900^3\) than \(800^3\)?
\(900^3 - 800^3 = 217,000,000\).
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 \(800^3\).
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?
The volume of the cube with a side length of 900 cm is 729,000,000 cm\(^3\).
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\(^3\).
Estimate the cube of 899 using the cube of 900.
The cube of 899 is approximately 729,000,000.
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.
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.
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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