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Question
Explain surds and give examples?
Explain surds and give examples?
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Solution
When we can't simplify a number to remove a square root (or cube root etc) then it is a surd.
Example: √2 (square root of 2) can't be simplified further so it is a surd
Example: √4 (square root of 4) can be simplified (to 2), so it is not a surd!
Have a look at some more examples:
Number Simplified As a Decimal Surd or
not? √2 √2 1.4142135...(etc) Surd √3 √3 1.7320508...(etc) Surd √4 2 2 Not a surd √¼ ½ 0.5 Not a surd 3√11 3√11 2.2239800...(etc) Surd 3√27 3 3 Not a surd 5√3 5√3 1.2457309...(etc) Surd
When we can't simplify a number to remove a square root (or cube root etc) then it is a surd.
Example: √2 (square root of 2) can't be simplified further so it is a surd
Example: √4 (square root of 4) can be simplified (to 2), so it is not a surd!
Have a look at some more examples:
Number Simplified As a Decimal Surd ornot?
| √2 | √2 | 1.4142135...(etc) | Surd |
| √3 | √3 | 1.7320508...(etc) | Surd |
| √4 | 2 | 2 | Not a surd |
| √¼ | ½ | 0.5 | Not a surd |
| 3√11 | 3√11 | 2.2239800...(etc) | Surd |
| 3√27 | 3 | 3 | Not a surd |
| 5√3 | 5√3 | 1.2457309...(etc) | Surd |
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