Summary
Powers and roots involve using indices to express repeated multiplication and finding roots as the inverse operation.
- Square — a number multiplied by itself. Example: 3 x 3 can be written as 3^2, which equals 9.
- Cube — a number multiplied by itself twice more. Example: 2 x 2 x 2 can be written as 2^3, which equals 8.
- Index form — notation using small digits to show powers. Example: 5^4 means 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: a number multiplied by itself
- Cube: a number multiplied by itself twice more
- Index form: notation using small digits to show powers
- 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
- Forgetting to add powers when multiplying indices with equal bases
Typical Exam Questions
- What is 3 squared? 9
- What is the cube root of 27? 3
- Simplify 2^3 x 2^2. 2^5 or 32
What Examiners Usually Test
- Understanding and using index form
- Calculating square and cube roots
- Applying the laws of indices correctly