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 870.
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 870 can be written as 870³, which is the exponential form. Or it can also be written in arithmetic form as, 870 × 870 × 870.
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. 870³ = 870 × 870 × 870 Step 2: You get 658,503,000 as the answer. Hence, the cube of 870 is 658,503,000.
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 870 into two parts. Let a = 800 and b = 70, so a + b = 870 Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³ Step 3: Calculate each term a³ = 800³ 3a²b = 3 × 800² × 70 3ab² = 3 × 800 × 70² b³ = 70³ Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (800 + 70)³ = 800³ + 3 × 800² × 70 + 3 × 800 × 70² + 70³ 870³ = 512,000,000 + 134,400,000 + 117,600,000 + 343,000 870³ = 658,503,000 Step 5: Hence, the cube of 870 is 658,503,000.
To find the cube of 870 using a calculator, input the number 870 and use the cube function (if available) or multiply 870 × 870 × 870. This operation calculates the value of 870³, resulting in 658,503,000. 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 7, then 0 Step 3: If the calculator has a cube function, press it to calculate 870³. Step 4: If there is no cube function on the calculator, simply multiply 870 three times manually. Step 5: The calculator will display 658,503,000.
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 870?
The cube of 870 is 658,503,000 and the cube root of 870 is approximately 9.546.
First, let’s find the cube of 870. 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 870³ = 658,503,000 Next, we must find the cube root of 870 We know that 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√870 ≈ 9.546 Hence the cube of 870 is 658,503,000 and the cube root of 870 is approximately 9.546.
If the side length of the cube is 870 cm, what is the volume?
The volume is 658,503,000 cm³.
Use the volume formula for a cube V = Side³. Substitute 870 for the side length: V = 870³ = 658,503,000 cm³.
How much larger is 870³ than 800³?
870³ – 800³ = 146,503,000.
First find the cube of 870³, that is 658,503,000 Next, find the cube of 800³, which is 512,000,000 Now, find the difference between them using the subtraction method. 658,503,000 – 512,000,000 = 146,503,000 Therefore, the 870³ is 146,503,000 larger than 800³.
If a cube with a side length of 870 cm is compared to a cube with a side length of 70 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 870 cm is 658,503,000 cm³
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object). Cubing 870 means multiplying 870 by itself three times: 870 × 870 = 756,900, and then 756,900 × 870 = 658,503,000. The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube. Therefore, the volume of the cube is 658,503,000 cm³.
Estimate the cube 869.9 using the cube 870.
The cube of 869.9 is approximately 658,503,000.
First, identify the cube of 870, The cube of 870 is 870³ = 658,503,000. Since 869.9 is only a tiny bit less than 870, the cube of 869.9 will be almost the same as the cube of 870. The cube of 869.9 is approximately 658,503,000 because the difference between 869.9 and 870 is very small. So, we can approximate the value as 658,503,000.
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. Volume of a Cube: The space inside a cube, calculated by raising the side length of the cube to the power of three. Perfect Cube: A number that can be expressed as the product of three identical integers. For example, 27 is a perfect cube because it is 3 × 3 × 3.
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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