103 LearnersLast updated on May 27th, 2025
Cube of 978
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 978.
Cube of 978
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 978 can be written as 978³, which is the exponential form. Or it can also be written in arithmetic form as 978 × 978 × 978.
How to Calculate the Value of Cube of 978
In order to check whether a number is a cube number or not, we can use the following three methods, such as the multiplication method, a factor formula (a³), or by using a calculator. These three methods will help in cubing the numbers faster and easier without feeling confused or stuck while evaluating the answers. By Multiplication Method Using a Formula Using a Calculator
By Multiplication Method
The multiplication method is a process in mathematics used to find the product of numbers by combining them through repeated multiplication. It is a fundamental operation that forms the basis for more complex mathematical concepts. Step 1: Write down the cube of the given number. 978³ = 978 × 978 × 978 Step 2: You get 936,681,752 as the answer. Hence, the cube of 978 is 936,681,752.
Using a Formula (a³)
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 978 into two parts, as a and b. Let a = 900 and b = 78, so a + b = 978 Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³ Step 3: Calculate each term a³ = 900³ 3a²b = 3 × 900² × 78 3ab² = 3 × 900 × 78² b³ = 78³ Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (900 + 78)³ = 900³ + 3 × 900² × 78 + 3 × 900 × 78² + 78³ 978³ = 729,000,000 + 189,540,000 + 16,489,200 + 474,552 978³ = 936,681,752 Step 5: Hence, the cube of 978 is 936,681,752.
Using a Calculator
To find the cube of 978 using a calculator, input the number 978 and use the cube function (if available) or multiply 978 × 978 × 978. This operation calculates the value of 978³, resulting in 936,681,752. 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 8 Step 3: If the calculator has a cube function, press it to calculate 978³. Step 4: If there is no cube function on the calculator, simply multiply 978 three times manually. Step 5: The calculator will display 936,681,752.
Tips and Tricks for the Cube of 978
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.
Common Mistakes to Avoid When Calculating the Cube of 978
There are some typical errors that might be made during the process of cubing a number. Let us take a look at five of the major mistakes that might occur:
Mistake 1
Incorrect Multiplication
One might multiply the numbers only twice, such as 978 × 978 and not 978 × 978 × 978. Always remember that 978³ = 978 × 978 × 978.
Solved Examples on Cube of 978
Problem 1
What is the cube and cube root of 978?
The cube of 978 is 936,681,752 and the cube root of 978 is approximately 9.812.
Explanation
First, let’s find the cube of 978. 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 978³ = 936,681,752 Next, we must find the cube root of 978 We know that the 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 ∛978 ≈ 9.812 Hence the cube of 978 is 936,681,752 and the cube root of 978 is approximately 9.812.
Problem 2
If the side length of the cube is 978 cm, what is the volume?
The volume is 936,681,752 cm³.
Explanation
Use the volume formula for a cube V = Side³. Substitute 978 for the side length: V = 978³ = 936,681,752 cm³.
Problem 3
How much larger is 978³ than 500³?
978³ – 500³ = 861,681,752.
Explanation
First, find the cube of 978³, which is 936,681,752 Next, find the cube of 500³, which is 125,000,000 Now, find the difference between them using the subtraction method. 936,681,752 – 125,000,000 = 811,681,752 Therefore, 978³ is 811,681,752 larger than 500³.
Problem 4
If a cube with a side length of 978 cm is compared to a cube with a side length of 100 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 978 cm is 936,681,752 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object). Cubing 978 means multiplying 978 by itself three times: 978 × 978 = 956,484, and then 956,484 × 978 = 936,681,752. The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube. Therefore, the volume of the cube is 936,681,752 cm³.
Problem 5
Estimate the cube 977.5 using the cube of 978.
The cube of 977.5 is approximately 936,681,752.
Explanation
First, identify the cube of 978, The cube of 978 is 978³ = 936,681,752. Since 977.5 is only a tiny bit less than 978, the cube of 977.5 will be almost the same as the cube of 978. The cube of 977.5 is approximately 936,681,752 because the difference between 977.5 and 978 is very small. So, we can approximate the value as 936,681,752.
FAQs on Cube of 978
1.What are the perfect cubes up to 978?
2.How do you calculate 978³?
3.What is the meaning of 978³?
4.What is the cube root of 978?
5.Is 978 a perfect cube?
6.How does learning Algebra help students in Canada make better decisions in daily life?
7.How can cultural or local activities in Canada support learning Algebra topics such as Cube of 978?
8.How do technology and digital tools in Canada support learning Algebra and Cube of 978?
9.Does learning Algebra support future career opportunities for students in Canada?
Important Glossaries for Cube of 978
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. 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. Perfect Cube: A number that can be expressed as the cube of an integer. Cube Root: The number that, when multiplied by itself three times, gives the original number.
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Jaskaran Singh Saluja
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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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