    ### 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

 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

#### What is the difference between √, 3√ and 4√?

 Root multiplied byitself 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

#### Examples

 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 to:   