Practice Questions on Cubes and Cube Roots with Solutions and Key Concepts
Class 8 mathematics is a crucial subject that you might need to study with proper assistance. You need to go to tutors, pay attention at school and do everything possible to get good marks in the examination.
One such chapter in Class 8 mathematics is Cubes and Cube Roots. This chapter is the boss level for the 8th standard students. There are many formulations that one must try and implement for finding the right answers to the questions asked from the chapter.
In this article, you will know about some of the core formulations of the chapter Cubes and Cube Roots.
Real Life Use of Cubes And Cube Roots
Every mathematics chapter is a fundamental theory that has been proved mathematically. Here are some details associated with the importance and application of cubes and cube roots.
This chapter is a fundamental theory that is proved with practical formulations. For instance, if a kid wants to count the number of cans stored that can be stored inside a cube-shaped box, then the cube root of the volume can get him/her the right answer. To make it easy to understand, cube root is the inverse procedure of finding the cube. You just have to reverse the finding method to get your cube root value. It will help you to get through class 8 maths chapter 7 cubes and cube roots MCQs.
Difference Between Square Root And Cube Root
When you multiply the number two times, it is stated as square root, and when you do it three times, it is termed to be as cube root. Hence, this is the difference between these two important chapters of class 8 mathematics.
Perfect Cube
Perfect cube resembles the whole number or integer as the ultimate cube root. For better clarity on understanding, the cube root value that does not have any decimal units is known as the perfect cube. For instance, 2 are the cube root of 8, hence 8 is the perfect cube.
Volume of A Cube
The volume of a cube has a specific formula, a3. The variable 'a' is the uniform sides of the cube. Here length is equal to the breadth, and both are equal to the height. Therefore, l=b=h is termed as 'a' in the formula. Hence, a3 is the volume of the cube. For instance, if all side of the cube is 5 cm then 5*5*5= 125 cm3.
How to Find A Cube Root of A Given Cube Number?
You need to follow certain specified steps to find the accurate cube root of the given cube value. As you know, the values multiplied three times with itself is called a cube. Cube root is the inverted figure that you need to derive whenever you get a question in your exams or test while you are in class 8.
Follow These Steps Precisely:
Pick the given number for which you need to find the cube root. Make groups of three digits starting from the right side of the given number.
Find the single one's unit from the first group, which will be the first part of the required cube root. For instance, the one's digit for the cube root of 53 is 3.
Now take the second group and apply the formula to find the two closest cubes within which the group value lies.
Now take the one's place of the extracted final number as the ten's position in the final cube root. Hence, you are ready to appear the questions for MCQ of ncert class 8 maths cubes and cube roots.
FAQs on Cubes and Cube Roots MCQs for Concept Mastery and Exam Practice
1. What is a cube number in Maths?
A cube number is a number obtained by multiplying a number by itself three times. In other words, if n is a number, its cube is n³ = n × n × n.
- Example: 2³ = 2 × 2 × 2 = 8
- Example: 5³ = 5 × 5 × 5 = 125
2. What is a cube root?
A cube root of a number is a value which, when multiplied by itself three times, gives the original number. It is written as ∛a.
- ∛27 = 3, because 3 × 3 × 3 = 27
- ∛125 = 5, because 5³ = 125
3. How do you find the cube of a number?
To find the cube of a number, multiply the number by itself three times. The formula is n³ = n × n × n.
- Step 1: Take the number (for example, 4).
- Step 2: Multiply 4 × 4 = 16.
- Step 3: Multiply 16 × 4 = 64.
4. How do you find the cube root of a perfect cube?
To find the cube root of a perfect cube, express the number as a product of three equal factors.
- Step 1: Prime factorize the number.
- Step 2: Group the factors in triples.
- Step 3: Take one factor from each group.
∛64 = 2 × 2 = 4.
5. What is the formula for cube and cube root?
The formula for cube is n³ = n × n × n and the formula for cube root is ∛a, where a = n³.
- If n = 6, then 6³ = 216.
- If a = 216, then ∛216 = 6.
6. What are the first 10 cube numbers?
The first 10 cube numbers are obtained by cubing numbers from 1 to 10.
- 1³ = 1
- 2³ = 8
- 3³ = 27
- 4³ = 64
- 5³ = 125
- 6³ = 216
- 7³ = 343
- 8³ = 512
- 9³ = 729
- 10³ = 1000
7. Is 729 a perfect cube?
Yes, 729 is a perfect cube because it can be written as 9 × 9 × 9.
- 9³ = 9 × 9 × 9 = 729
- Therefore, ∛729 = 9.
8. What is the cube root of a negative number?
The cube root of a negative number is negative because the product of three negative numbers is negative.
- (−3)³ = −27
- So, ∛(−27) = −3.
9. What is the difference between a cube and a cube root?
The cube of a number means multiplying it by itself three times, while the cube root finds the number that was multiplied three times.
- Cube: 4³ = 64
- Cube root: ∛64 = 4
10. How do you solve cubes and cube roots MCQs quickly?
To solve cubes and cube roots MCQs quickly, memorize common cubes and use factorization techniques.
- Learn cubes from 1 to 20 for faster calculation.
- Use prime factorization to find cube roots.
- Check the last digit pattern of cube numbers.
- Eliminate incorrect options using estimation.
