Squares and square roots
- A square number is a number multiplied by itself: 7² = 49.
- Learn the squares up to 15²: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225.
- The square root undoes squaring: √49 = 7. Every positive number has two square roots: 7 and −7.
Cubes and cube roots
- A cube number is a number multiplied by itself three times: 4³ = 64.
- Learn 1, 8, 27, 64, 125 and 1000. The cube root undoes cubing: ∛125 = 5.
- Negative numbers have a negative cube root: ∛(−8) = −2.
Other powers
- 2⁵ = 2 × 2 × 2 × 2 × 2 = 32; 3⁴ = 81.
- Powers of 10: 10² = 100, 10³ = 1000, 10⁶ = 1 000 000.
Estimating roots
- √50 lies between √49 = 7 and √64 = 8, and is closer to 7.
- Use the square numbers either side to estimate a square root.
Key terms
- Square number
- The result of multiplying a whole number by itself.
- Square root
- The number that multiplies by itself to give the original number.
- Cube number
- The result of multiplying a whole number by itself three times.
- Cube root
- The number that multiplied by itself three times gives the original number.
- Power
- The small raised number showing how many times to multiply a number by itself.
- Index
- Another word for power (plural: indices).