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 when comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of 817.
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 817 can be written as 817³, which is the exponential form. Or it can also be written in arithmetic form as 817 × 817 × 817.
In order 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 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. 817³ = 817 × 817 × 817 Step 2: You get 544,399,513 as the answer. Hence, the cube of 817 is 544,399,513.
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 817 into two parts, as 800 and 17. Let a = 800 and b = 17, so a + b = 817 Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³ Step 3: Calculate each term a³ = 800³ 3a²b = 3 × 800² × 17 3ab² = 3 × 800 × 17² b³ = 17³ Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (800 + 17)³ = 800³ + 3 × 800² × 17 + 3 × 800 × 17² + 17³ 817³ = 512,000,000 + 32,640,000 + 694,800 + 4,913 817³ = 544,399,513 Step 5: Hence, the cube of 817 is 544,399,513.
To find the cube of 817 using a calculator, input the number 817 and use the cube function (if available) or multiply 817 × 817 × 817. This operation calculates the value of 817³, resulting in 544,399,513. It’s a quick way to determine the cube without manual computation. Step 1: Ensure the calculator is functioning properly. Step 2: Input 8, then 1, followed by 7 Step 3: If the calculator has a cube function, press it to calculate 817³. Step 4: If there is no cube function on the calculator, simply multiply 817 three times manually. Step 5: The calculator will display 544,399,513.
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 817?
The cube of 817 is 544,399,513 and the cube root of 817 is approximately 9.444.
First, let’s find the cube of 817. We know that the cube of a number is such that x³ = y Where x is the given number, and y is the cubed value of that number So, we get 817³ = 544,399,513 Next, we must find the cube root of 817 We know that the cube root of a number ‘x’ is such that ∛x = y So, we get ∛817 ≈ 9.444 Hence, the cube of 817 is 544,399,513 and the cube root of 817 is approximately 9.444.
If the side length of the cube is 817 cm, what is the volume?
The volume is 544,399,513 cm³.
Use the volume formula for a cube V = Side³. Substitute 817 for the side length: V = 817³ = 544,399,513 cm³.
How much larger is 817³ than 800³?
817³ – 800³ = 32,399,513.
First find the cube of 817, which is 544,399,513 Next, find the cube of 800, which is 512,000,000 Now, find the difference between them using the subtraction method. 544,399,513 – 512,000,000 = 32,399,513 Therefore, 817³ is 32,399,513 larger than 800³.
If a cube with a side length of 817 cm is compared to a cube with a side length of 17 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 817 cm is 544,399,513 cm³.
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object). Cubing 817 means multiplying 817 by itself three times: 817 × 817 = 667,489, and then 667,489 × 817 = 544,399,513. The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube. Therefore, the volume of the cube is 544,399,513 cm³.
Estimate the cube of 816.5 using the cube of 817.
The cube of 816.5 is approximately 544,399,513.
First, identify the cube of 817, The cube of 817 is 817³ = 544,399,513. Since 816.5 is very close to 817, the cube of 816.5 will be nearly the same as the cube of 817. The cube of 816.5 is approximately 544,399,513 because the difference between 816.5 and 817 is very small. So, we can approximate the value as 544,399,513.
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: The amount of space occupied by a 3-dimensional object, calculated for a cube as side³. Cube Root: The cube root of a number is a value that, when multiplied by itself three times, gives the original number.
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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