What are Surds?
A surd is a "square root", "cube root" etc of a number that is not a whole number. Where the value of the decimal goes on for ever... that is to infinity. Surds are irrational numbers.
- Demonstration of Surds
- What is the difference between √, 3√ and 4√?
- Examples
| Surd | Same as | Value | Is it a surd? |
| √4 | 4½ | 2 | No |
| √8 | 8½ | 2.828427125... | Yes |
| √12 | 12½ | 3.464101615... | Yes |
| √16 | 16½ | 4 | No |
| √20 | 20½ | 4.472135955... | Yes |
| 3√8 | 81/3 | 2 | No |
| 3√16 | 161/3 | 2.51984209... | Yes |
| 3√20 | 201/3 | 2.714417617... | Yes |
| 3√27 | 271/3 | 3 | No |
| 4√16 | 16¼ | 2 | No |
| 4√50 | 50¼ | 2.659147948... | Yes |
| 4√81 | 81¼ | 3 | No |
| Root | multiplied by itself | |
| square root | √3 × √3 = 3 Or 3½ × 3½ = 3 | twice |
| cube root | 3√4 × 3√4 × 3√4 = 4 Or 41/3 × 41/3 × 41/3 = 4 | three times |
| root | 4√7 × 4√7 × 4√7 × 4√7 = 7 Or 7¼ × 7¼ × 7¼ × 7¼ = 7 | four times |
| e.g. | Multiply a surd by itself | Surd? | |
| 1. | √4 | √4 × √4 = 4 Or 2 × 2 = 4 | no |
| 2. | √8 | √8 × √8 = 8 Or 2.828427125 × 2.828427125 = 8 | yes |
| 3. | √12 | √12 × √12 = 12 Or 3.464101615 × 3.464101615 = 12 | yes |
| 4. | √16 | √16 × √16 = 16 Or 4 × 4 = 16 | no |
| 5. | √20 | √20 × √20 = 20 Or 4.472135955 × 4.472135955 = 20 | yes |
| 6. | 3√8 | 3√8 × 3√8 × 3√8 = 8 Or 2 × 2 × 2 = 20 | no |
| 7. | 3√16 | 3√16 × 3√16 × 3√16 = 16 Or 2.51984209 × 2.51984209 × 2.51984209 = 16 | yes |
| 8. | 3√20 | 3√20 × 3√20 × 3√20 = 20 Or 2.714417617 × 2.714417617 × 2.714417617 = 20 | yes |
| 9. | 3√27 | 3√27 × 3√27 × 3√27 = 27 Or 3 × 3 × 3 = 27 | no |
| 10. | 4√16 | 4√16 × 4√16 × 4√16 × 4√16 = 16 Or 2 × 2 × 2 × 2 = 16 | no |
| 11. | 4√50 | 4√50 × 4√50 × 4√50 × 4√50 = 50 Or 2.659147948 × 2.659147948 × 2.659147948 × 2.659147948 = 50 | yes |
| 12. | 4√81 | 4√81 × 4√81 × 4√81 × 4√81 = 81 Or 3 × 3 × 3 × 3 = 81 | no |
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