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 cubes of 827.
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 827 can be written as 827³, which is the exponential form. Or it can also be written in arithmetic form as, 827 × 827 × 827.
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
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. 827³ = 827 × 827 × 827 Step 2: You get 565,231,283 as the answer. Hence, the cube of 827 is 565,231,283.
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 827 into two parts, as 800 and 27. Let a = 800 and b = 27, so a + b = 827 Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³ Step 3: Calculate each term a³ = 800³ 3a²b = 3 × 800² × 27 3ab² = 3 × 800 × 27² b³ = 27³ Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (800 + 27)³ = 800³ + 3 × 800² × 27 + 3 × 800 × 27² + 27³ 827³ = 512,000,000 + 51,840,000 + 17,496,000 + 19,683 827³ = 565,231,283 Step 5: Hence, the cube of 827 is 565,231,283.
To find the cube of 827 using a calculator, input the number 827 and use the cube function (if available) or multiply 827 × 827 × 827. This operation calculates the value of 827³, resulting in 565,231,283. 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 2 and 7 Step 3: If the calculator has a cube function, press it to calculate 827³. Step 4: If there is no cube function on the calculator, simply multiply 827 three times manually. Step 5: The calculator will display 565,231,283.
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 827?
The cube of 827 is 565,231,283 and the cube root of 827 is approximately 9.42.
First, let’s find the cube of 827. 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 827³ = 565,231,283 Next, we must find the cube root of 827 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 ∛827 ≈ 9.42 Hence the cube of 827 is 565,231,283 and the cube root of 827 is approximately 9.42.
If the side length of the cube is 827 cm, what is the volume?
The volume is 565,231,283 cm³.
Use the volume formula for a cube V = Side³. Substitute 827 for the side length: V = 827³ = 565,231,283 cm³.
How much larger is 827³ than 727³?
827³ – 727³ = 276,283,283.
First find the cube of 827, that is 565,231,283 Next, find the cube of 727, which is 288,948,000 Now, find the difference between them using the subtraction method. 565,231,283 – 288,948,000 = 276,283,283 Therefore, 827³ is 276,283,283 larger than 727³.
If a cube with a side length of 827 cm is compared to a cube with a side length of 627 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 827 cm is 565,231,283 cm³.
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object). Cubing 827 means multiplying 827 by itself three times: 827 × 827 = 683,929, and then 683,929 × 827 = 565,231,283. The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube. Therefore, the volume of the cube is 565,231,283 cm³.
Estimate the cube of 826.9 using the cube of 827.
The cube of 826.9 is approximately 565,231,283.
First, identify the cube of 827, The cube of 827 is 827³ = 565,231,283. Since 826.9 is only a tiny bit less than 827, the cube of 826.9 will be almost the same as the cube of 827. The cube of 826.9 is approximately 565,231,283 because the difference between 826.9 and 827 is very small. So, we can approximate the value as 565,231,283.
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. Perfect Cube: A number that can be expressed as the product of three identical factors is called a perfect cube. Calculator Function: A feature available in digital calculators that allows for quick calculations of powers and roots.
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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