Squares, cubes and roots
- 7² = 7 × 7 = 49, and √49 = 7. Every positive number has two square roots: 6 and −6 both square to 36.
- 4³ = 4 × 4 × 4 = 64, and the cube root of 64 is 4.
- Estimate roots using square numbers: √50 is between 7 and 8, because 49 < 50 < 64.
Powers
- 2⁵ means 2 × 2 × 2 × 2 × 2 = 32. The small number is the power (or index).
- Multiplying powers of the same number: add the powers: 3⁴ × 3² = 3⁶.
- Dividing: subtract the powers: 5⁷ ÷ 5³ = 5⁴.
- A power of a power: multiply the powers: (2³)² = 2⁶.
- Any number (except 0) to the power 0 is 1: 10⁰ = 1.
Order of operations
- BIDMAS: Brackets, Indices (powers), then Division and Multiplication (left to right), then Addition and Subtraction (left to right).
- 3 + 4 × 2 = 3 + 8 = 11, but (3 + 4) × 2 = 14.
- 3 + 4 × 2² = 3 + 4 × 4 = 3 + 16 = 19.
Key terms
- Square number
- A number multiplied by itself.
- Square root
- A number that multiplies by itself to give the original number.
- Cube number
- A number multiplied by itself twice.
- Cube root
- A number that cubes to give the original number.
- Power (index)
- The small number that shows how many times to multiply a number by itself.
- Index laws
- Rules for multiplying and dividing powers of the same number.
- BIDMAS
- The order of operations: brackets, indices, division and multiplication, addition and subtraction.