Powers and roots · Year 10
In Year 10 you learn: fractional powers and surds.
A power tells you how many times to multiply a number by itself: 5^2 = 5 × 5 and 2^3 = 2 × 2 × 2. Square roots and cube roots undo squaring and cubing. Squares and cubes appear whenever we work with area and volume.
Key facts
- a^2 means a × a (a squared); a^3 means a × a × a (a cubed). Not a × 2!
- Square numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 …
- Cube numbers: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1,000 …
- A negative number squared is positive: (−4)^2 = 16, but −4^2 = −16.