Study Notes
Powers and roots involve using indices to express repeated multiplication and finding the original number from its power.
- Square — a number multiplied by itself. Example: 3 x 3 = 9 can be written as 3².
- Cube — a number multiplied by itself twice. Example: 2 x 2 x 2 = 8 can be written as 2³.
- Index form — notation using a base and an index number to show repeated multiplication. Example: 5⁴ = 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 three times in multiplication, gives the original number. Example: ∛27 = 3 because 3 x 3 x 3 = 27.
- Laws of indices — rules for operations with powers, such as adding indices when multiplying like bases.
Exam Tips
Key Definitions to Remember
- Square: a number multiplied by itself
- Cube: a number multiplied by itself twice
- Index form: notation using a base and an index number
- Square root: the number that gives the original number when squared
- Cube root: the number that gives the original number when cubed
Common Confusions
- Confusing square and cube roots
- Misapplying the laws of indices
Typical Exam Questions
- What is 3 squared? 9
- What is the cube root of 64? 4
- Simplify 2³ x 2². 2⁵
What Examiners Usually Test
- Understanding of index notation
- Ability to calculate powers and roots
- Application of the laws of indices