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 824.
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 824 can be written as 824³, which is the exponential form. Or it can also be written in arithmetic form as, 824 × 824 × 824.
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 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. 824³ = 824 × 824 × 824 Step 2: Calculate the multiplication to get the answer. Hence, the cube of 824 is 558,476,544.
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 824 into two parts, as 800 and 24. Let a = 800 and b = 24, so a + b = 824 Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³ Step 3: Calculate each term a³ = 800³ 3a²b = 3 × 800² × 24 3ab² = 3 × 800 × 24² b³ = 24³ Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (800 + 24)³ = 800³ + 3 × 800² × 24 + 3 × 800 × 24² + 24³ 824³ = 512,000,000 + 46,080,000 + 460,800 + 13,824 824³ = 558,476,544 Step 5: Hence, the cube of 824 is 558,476,544.
To find the cube of 824 using a calculator, input the number 824 and use the cube function (if available) or multiply 824 × 824 × 824. This operation calculates the value of 824³, resulting in 558,476,544. 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 4 Step 3: If the calculator has a cube function, press it to calculate 824³. Step 4: If there is no cube function on the calculator, simply multiply 824 three times manually. Step 5: The calculator will display 558,476,544.
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 824?
The cube of 824 is 558,476,544, and the cube root of 824 is approximately 9.442.
First, let’s find the cube of 824. 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 824³ = 558,476,544 Next, we must find the cube root of 824 We know that the cube root of a number ‘x’, such that ³√x = y Where ‘x’ is the given number, and y is the cube root value of the number So, we get ³√824 ≈ 9.442 Hence the cube of 824 is 558,476,544, and the cube root of 824 is approximately 9.442.
If the side length of the cube is 824 cm, what is the volume?
The volume is 558,476,544 cm³.
Use the volume formula for a cube V = Side³. Substitute 824 for the side length: V = 824³ = 558,476,544 cm³.
How much larger is 824³ than 400³?
824³ – 400³ = 558,476,544 - 64,000,000 = 494,476,544.
First, find the cube of 824³, that is 558,476,544. Next, find the cube of 400³, which is 64,000,000. Now, find the difference between them using the subtraction method. 558,476,544 - 64,000,000 = 494,476,544. Therefore, 824³ is 494,476,544 larger than 400³.
If a cube with a side length of 824 cm is compared to a cube with a side length of 10 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 824 cm is 558,476,544 cm³.
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object). Cubing 824 means multiplying 824 by itself three times: 824 × 824 = 678,976, and then 678,976 × 824 = 558,476,544. The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube. Therefore, the volume of the cube is 558,476,544 cm³.
Estimate the cube of 823 using the cube of 824.
The cube of 823 is approximately 558,476,544.
First, identify the cube of 824, The cube of 824 is 824³ = 558,476,544. Since 823 is only a tiny bit less than 824, the cube of 823 will be almost the same as the cube of 824. The cube of 823 is approximately 558,476,544 because the difference between 823 and 824 is very small. So, we can approximate the value as 558,476,544.
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. Multiplication Method: A mathematical process used to find the product of numbers or quantities by combining them through repeated addition. Perfect Cube: A number that can be expressed as the cube of an integer.
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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