Case Study Questions for Class 8 Maths Chapter 7 Cube and Cube Roots
Here we are providing Case Study questions for Class 8 Maths Chapter 7 Cube and Cube Roots.
Table of Contents
| Maths Class 8 Chapter 7 | Cube and Cube Roots |
|---|---|
| Maths | CBSE Class 8 |
| Chapter Covered | Class 8 Maths Chapter 7 |
| Topics | Cubes Adding Consecutive Odd Numbers Cubes and their Prime Factors Cube Roots |
| Type of Questions | Case Study Questions |
| Questions with Answers | Yes, answers provided |
| Important Keywords | Provided in the end |
Case Study Questions
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CBSE Class 8 Maths Chapter 7 Cube and Cube Roots
Learning Outcomes
- (i) Calculating the cubes of non-zero numbers
- (ii) Finding the relation between unit digit of a number and its cube.
- (iii) Calculating the cube roots using different methods.
Important Keywords
- Cubes: The cube of a number is that number raised to the power 3. If x is a number, then x3 = x × x × x.
- Cubes root: The cube root of a number x is the number whose cube is x.
More Keywords
Cubes:
1. Cube of a number: The result when a number is raised to the power of 3.
Example: The cube of 2 is \(2^3 = 2 \times 2 \times 2 = 8\).
2. Perfect cubes: Numbers that are the result of cubing a whole number.
Example: 8, 27, 64 are perfect cubes.
3. Cubic numbers: Numbers that can be represented as \(a^3\) for some integer \(a\).
Example: 125 is a cubic number since \(5^3 = 125\).
4. Cube of a negative integer: The result when a negative number is raised to the power of 3.
Example: The cube of \(-3\) is \((-3)^3 = -3 \times -3 \times -3 = -27\).
5. Volume of a cube: The amount of space occupied by a cube, calculated as \(side \times side \times side\).
Example: If the side length of a cube is 4 units, its volume is \(4 \times 4 \times 4 = 64\) cubic units.
Cube Roots:
1. Cube root of a number: A value that, when raised to the power of 3, gives the original number.
Example: The cube root of 27 is \(\sqrt[3]{27} = 3\) since \(3^3 = 27\).
2. Estimating cube roots: Approximating the value of a cube root.
Example: Estimating \(\sqrt[3]{18}\) could yield an approximate value of 2 because \(2^3 = 8\) is close to 18.
3. Cube root notation: Represented as \(\sqrt[3]{a}\), where \(a\) is the number for which the cube root is being calculated.
Example: \(\sqrt[3]{64}\) represents the cube root of 64.
4. Cube root of fractions and decimals: Calculating the cube root of fractional or decimal numbers.
Example: \(\sqrt[3]{0.125} = 0.5\) since \(0.5^3 = 0.125\).
5. Cube root of a perfect cube: Finding the cube root of a number that is a perfect cube.
Example: The cube root of 125 is \(\sqrt[3]{125} = 5\) since \(5^3 = 125\).
6. Solving cube root equations: Finding the value(s) that satisfy equations involving cube roots.
Example: Solving the equation \(\sqrt[3]{x} = 4\) gives \(x = 64\) as the cube root of 64 is 4.
Important Facts
- A natural number n is a perfect cube if n = m3 for some natural number m.
- The cube of an even natural number is even.
- The cube of an odd natural number is odd.
- The cube of a negative number is always negative.
- Cubes of the numbers ending with the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 end with digits 0, 1, 8, 1, 7, 5, 6, 3, 2, 9 respectively. Here, cubes of numbers ending with digits 0, 1, 4, 5, 6 and 9 end with same digits.
- Cubes of the number ending with digit 2 ends in 8 or cube of the number ending with digit 8 ends in 2.
- Cube of the number ending with digit 3 ends in 7 and cube of the number ending with digit 7 ends in 3.
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