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 975.
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 multiplied by itself three times results in a negative number. The cube of 975 can be written as 975³, which is the exponential form. Or it can also be written in arithmetic form as, 975 × 975 × 975.
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 methods will help kids 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 in mathematics is used to find the product of numbers 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. 975³ = 975 × 975 × 975 Step 2: You get 926,859,375 as the answer. Hence, the cube of 975 is 926,859,375.
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 975 into two parts, as 900 and 75. Let a = 900 and b = 75, so a + b = 975 Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³ Step 3: Calculate each term a³ = 900³ 3a²b = 3 × 900² × 75 3ab² = 3 × 900 × 75² b³ = 75³ Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (900 + 75)³ = 900³ + 3 × 900² × 75 + 3 × 900 × 75² + 75³ 975³ = 729,000,000 + 182,250,000 + 151,875,000 + 421,875 975³ = 926,859,375 Step 5: Hence, the cube of 975 is 926,859,375.
To find the cube of 975 using a calculator, input the number 975 and use the cube function (if available) or multiply 975 × 975 × 975. This operation calculates the value of 975³, resulting in 926,859,375. It’s a quick way to determine the cube without manual computation. Step 1: Ensure the calculator is functioning properly. Step 2: Press 9 followed by 7 and 5 Step 3: If the calculator has a cube function, press it to calculate 975³. Step 4: If there is no cube function on the calculator, simply multiply 975 three times manually. Step 5: The calculator will display 926,859,375.
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 975?
The cube of 975 is 926,859,375 and the cube root of 975 is approximately 9.861.
First, let’s find the cube of 975. 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 975³ = 926,859,375 Next, we must find the cube root of 975 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√975 ≈ 9.861 Hence the cube of 975 is 926,859,375 and the cube root of 975 is approximately 9.861.
If the side length of the cube is 975 cm, what is the volume?
The volume is 926,859,375 cm³.
Use the volume formula for a cube V = Side³. Substitute 975 for the side length: V = 975³ = 926,859,375 cm³.
How much larger is 975³ than 900³?
975³ – 900³ = 197,859,375.
First, find the cube of 975, which is 926,859,375. Next, find the cube of 900, which is 729,000,000. Now, find the difference between them using the subtraction method. 926,859,375 – 729,000,000 = 197,859,375 Therefore, 975³ is 197,859,375 larger than 900³.
If a cube with a side length of 975 cm is compared to a cube with a side length of 75 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 975 cm is 926,859,375 cm³.
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object). Cubing 975 means multiplying 975 by itself three times: 975 × 975 = 950,625, and then 950,625 × 975 = 926,859,375. The unit of volume is cubic centimeters (cm³) because we are calculating the space inside the cube. Therefore, the volume of the cube is 926,859,375 cm³.
Estimate the cube of 974 using the cube of 975.
The cube of 974 is approximately 926,859,375.
First, identify the cube of 975, The cube of 975 is 975³ = 926,859,375. Since 974 is only a tiny bit less than 975, the cube of 974 will be almost the same as the cube of 975. The cube of 974 is approximately 926,859,375 because the difference between 974 and 975 is very small. So, we can approximate the value as 926,859,375.
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 equals 8. Cube Root: A number that when multiplied by itself three times gives the original number. For example, the cube root of 8 is 2. Perfect Cube: A number that can be expressed as the cube of an integer. For instance, 27 is a perfect cube because it is 3³.
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.
: He loves to play the quiz with kids through algebra to make kids love it.