Reducing Surds
Reducing surds are also called simplifying surds. Surds can be reduced if they contain a perfect square as a factor
- Example 1. Simplify the surd √8
- Example 2. Reduce the surd √20
- Example 3. Simplify the surd √432
- Example 4. Reduce the surd √1350
| √8 | = | √(4 × 2) | ||
| = | √4 × √2 | note √4 = 2 so | ||
| = | 2 √2 | |||
| √20 | = | √(4 × 5) | ||
| = | √4 × √5 | note √4=2 so | ||
| = | 2 √5 | |||
| (a) | List the perfect squares | ||||||||||||||||
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| (b) | From (a) the GREEN ones below are factors of 432 | ||||||||||||||||
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| (c) | From (b) choose the largest perfect square 36 | ||||||||||||||||
| (d) | Carry on as before | ||||||||||||||||
| √432 | = | √(36 × 12) = 6√12 | |
| = | 6√(4 × 3) = 6.2√3 | ||
| = | 12√3 |
| (a) | List the perfect squares | ||||||||||||||||
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| (b) | From (a) the GREEN ones below are factors of 1350 | ||||||||||||||||
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| (c) | From (b) choose the largest perfect square 25 | ||||||||||||||||
| (d) | Carry on as before | ||||||||||||||||
| √1350 | = | √(25 × 54) = 5√54 | |
| = | 5√(9 × 6) = 5.3√6 | ||
| = | 15√6 |
Remember: reduce the surd and simplify the surd are the same thing
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