Study Notes
Powers and roots involve using indices to express repeated multiplication and finding roots as the inverse operation.
- Square Number — A number multiplied by itself. Example: 3 x 3 = 9, which can be written as 3^2.
- Cube Number — A number multiplied by itself twice more. Example: 2 x 2 x 2 = 8, which can be written as 2^3.
- Index Form — A way to write powers using a base and an index. Example: 5^4 = 5 x 5 x 5 x 5 = 625.
- Square Root — The number that, when multiplied by itself, gives the original number. Example: √16 = 4 because 4 x 4 = 16.
- Cube Root — The number that, when used in threefold multiplication, gives the original number. Example: ∛27 = 3 because 3 x 3 x 3 = 27.
- Laws of Indices — Rules for operations with powers. Example: When multiplying indices with equal bases, add the powers.
Exam Tips
Key Definitions to Remember
- Square Number: A number multiplied by itself.
- Cube Number: A number multiplied by itself twice more.
- Index Form: A way to write powers using a base and an index.
- Square Root: The number that, when multiplied by itself, gives the original number.
- Cube Root: The number that, when used in threefold multiplication, gives the original number.
Common Confusions
- Confusing square roots with cube roots.
- Forgetting to add powers when multiplying indices with the same base.
Typical Exam Questions
- What is 3 squared? Answer: 9
- What is the cube root of 1,000? Answer: 10
- Simplify 2^3 x 2^4. Answer: 2^7
What Examiners Usually Test
- Understanding of index form and how to use it.
- Ability to calculate square and cube roots.
- Application of the laws of indices in simplifying expressions.