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 840.
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 840 can be written as 840³, which is the exponential form. Or it can also be written in arithmetic form as, 840 × 840 × 840.
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 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. 840³ = 840 × 840 × 840 Step 2: You get 592,704,000 as the answer. Hence, the cube of 840 is 592,704,000.
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 840 into two parts, as 800 and 40. Let a = 800 and b = 40, so a + b = 840 Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³ Step 3: Calculate each term a³ = 800³ 3a²b = 3 × 800² × 40 3ab² = 3 × 800 × 40² b³ = 40³ Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (800 + 40)³ = 800³ + 3 × 800² × 40 + 3 × 800 × 40² + 40³ 840³ = 512,000,000 + 76,800,000 + 38,400,000 + 64,000 840³ = 592,704,000 Step 5: Hence, the cube of 840 is 592,704,000.
To find the cube of 840 using a calculator, input the number 840 and use the cube function (if available) or multiply 840 × 840 × 840. This operation calculates the value of 840³, resulting in 592,704,000. It’s a quick way to determine the cube without manual computation. Step 1: Ensure the calculator is functioning properly. Step 2: Input 840 Step 3: If the calculator has a cube function, press it to calculate 840³. Step 4: If there is no cube function on the calculator, simply multiply 840 three times manually. Step 5: The calculator will display 592,704,000.
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 might occur during the process of cubing a number. Let us take a look at five of the major mistakes that might occur:
What is the cube and cube root of 840?
The cube of 840 is 592,704,000 and the cube root of 840 is approximately 9.434.
First, let’s find the cube of 840. We know that 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 840³ = 592,704,000 Next, we must find the cube root of 840 We know that 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 ∛840 ≈ 9.434 Hence, the cube of 840 is 592,704,000 and the cube root of 840 is approximately 9.434.
If the side length of the cube is 840 cm, what is the volume?
The volume is 592,704,000 cm³.
Use the volume formula for a cube V = Side³. Substitute 840 for the side length: V = 840³ = 592,704,000 cm³.
How much larger is 840³ than 740³?
840³ – 740³ = 326,496,000.
First, find the cube of 840³, which is 592,704,000. Next, find the cube of 740³, which is 266,208,000. Now, find the difference between them using the subtraction method. 592,704,000 – 266,208,000 = 326,496,000 Therefore, the 840³ is 326,496,000 larger than 740³.
If a cube with a side length of 840 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 840 cm is 592,704,000 cm³.
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object). Cubing 840 means multiplying 840 by itself three times: 840 × 840 = 705,600, and then 705,600 × 840 = 592,704,000. The unit of volume is cubic centimeters (cm³) because we are calculating the space inside the cube. Therefore, the volume of the cube is 592,704,000 cm³.
Estimate the cube of 839.5 using the cube of 840.
The cube of 839.5 is approximately 592,704,000.
First, identify the cube of 840, The cube of 840 is 840³ = 592,704,000. Since 839.5 is very close to 840, the cube of 839.5 will be almost the same as the cube of 840. The cube of 839.5 is approximately 592,704,000 because the difference between 839.5 and 840 is very small. So, we can approximate the value as 592,704,000.
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, 2³ represents 2 × 2 × 2 equals 8. Cube Root: The number which, when multiplied by itself three times, gives the original number. Volume of a Cube: The amount of space occupied by a cube, calculated using the formula V = Side³, where 'Side' is the length of a side of the cube.
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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