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 972.
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 972 can be written as 972³, which is the exponential form. Or it can also be written in arithmetic form as 972 × 972 × 972.
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. 972³ = 972 × 972 × 972 Step 2: You get 917,338,673 as the answer. Hence, the cube of 972 is 917,338,673.
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 972 into two parts. Let a = 970 and b = 2, so a + b = 972. Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³. Step 3: Calculate each term: a³ = 970³ 3a²b = 3 × 970² × 2 3ab² = 3 × 970 × 2² b³ = 2³ Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (970 + 2)³ = 970³ + 3 × 970² × 2 + 3 × 970 × 2² + 2³ 972³ = 912,673,000 + 5,642,800 + 11,640 + 8 972³ = 917,338,673 Step 5: Hence, the cube of 972 is 917,338,673.
To find the cube of 972 using a calculator, input the number 972 and use the cube function (if available) or multiply 972 × 972 × 972. This operation calculates the value of 972³, resulting in 917,338,673. It’s a quick way to determine the cube without manual computation. Step 1: Ensure the calculator is functioning properly. Step 2: Press 9, 7, and 2. Step 3: If the calculator has a cube function, press it to calculate 972³. Step 4: If there is no cube function on the calculator, simply multiply 972 three times manually. Step 5: The calculator will display 917,338,673.
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 972?
The cube of 972 is 917,338,673 and the cube root of 972 is approximately 9.872.
First, let’s find the cube of 972. 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 972³ = 917,338,673. Next, we must find the cube root of 972. 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√972 ≈ 9.872. Hence, the cube of 972 is 917,338,673 and the cube root of 972 is approximately 9.872.
If the side length of the cube is 972 cm, what is the volume?
The volume is 917,338,673 cm³.
Use the volume formula for a cube V = Side³. Substitute 972 for the side length: V = 972³ = 917,338,673 cm³.
How much larger is 972³ than 970³?
972³ – 970³ = 5,686,673.
First, find the cube of 972, that is 917,338,673. Next, find the cube of 970, which is 912,673,000. Now, find the difference between them using the subtraction method. 917,338,673 – 912,673,000 = 5,686,673. Therefore, 972³ is 5,686,673 larger than 970³.
If a cube with a side length of 972 cm is compared to a cube with a side length of 2 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 972 cm is 917,338,673 cm³.
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object). Cubing 972 means multiplying 972 by itself three times: 972 × 972 = 945,784, and then 945,784 × 972 = 917,338,673. The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube. Therefore, the volume of the cube is 917,338,673 cm³.
Estimate the cube 971.9 using the cube 972.
The cube of 971.9 is approximately 917,338,673.
First, identify the cube of 972. The cube of 972 is 972³ = 917,338,673. Since 971.9 is only a tiny bit less than 972, the cube of 971.9 will be almost the same as the cube of 972. The cube of 971.9 is approximately 917,338,673 because the difference between 971.9 and 972 is very small. So, we can approximate the value as 917,338,673.
Binomial Formula: 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: 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, which equals 8. Volume: The amount of space occupied by a 3-dimensional object, calculated as the product of its dimensions, such as length, width, and height. 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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