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- 1. Surds Surds Objectives In this lesson, we will learn to <ul><li>multiply, divide, add and subtract surds, </li></ul><ul><li>simplify expressions with surds, </li></ul><ul><li>rationalise a fraction whose denominator is a surd, </li></ul><ul><li>solve equations involving surds. </li></ul>
- 2. is the positive square root of k , for positive values of k . The following rules apply: Let’s apply these rules to simplifying some expressions. Surds
- 3. Surds Simplify Simplify Combine the square roots. Example
- 4. Surds Simplify Simplify Applies to the product of any number of terms. Example
- 5. Surds Simplify Example
- 6. Surds Simplify Simplify Factorise. Factorise. Example Express each term in terms of
- 7. Surds Simplify Expand. Collect terms. Example
- 8. Surds Simplify Rationalise the denominator. Equivalent form Equivalent to multiplying by 1. Example
- 9. Surds Simplify Equivalent to multiplying by 1. Difference of two squares. Alternate form of the answer. This will rationalise the denominator. Example
- 10. Surds, Indices and Logarithms Simplify Equivalent to multiplying by 1. Rationalise the denominator. Example
- 11. Surds, Indices and Logarithms Solve the equation Check Square both sides of the equation. This clears the surds. Example
- 12. Surds, Indices and Logarithms Summary 1: Rationalising the Denominator You can swap the ‘ –’ and the ‘+’ signs. If the denominator contains Multiply by If the denominator contains Multiply by
- 13. Surds Solve the equation Check Rearrange the equation and square both sides. This clears the surds. Solve the equation. A check is always needed due to squaring. Example
- 14. If we square both sides of an equation then the following can happen: So, solving the equation may give us a different solution. Obviously both cannot be correct. Surds . . ,
- 15. Another rule to apply to the equality of surds Let’s apply this rule to solving an equation. Surds
- 16. Find the values of a and b . Equating rational and irrational terms. Solve like solving a pair of simultaneous equations. Expand LHS. Surds Example Solution

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