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Surds

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• 2.1 Surds Objectives In this lesson we will learn about multiplication, division, addition and subtraction of surds; about simplification; about rationalising the denominator and about solving equations involving surds.
• Surds

1. 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. 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. 3. Surds Simplify Simplify Combine the square roots. Example
4. 4. Surds Simplify Simplify Applies to the product of any number of terms. Example
5. 5. Surds Simplify Example
6. 6. Surds Simplify Simplify Factorise. Factorise. Example Express each term in terms of
7. 7. Surds Simplify Expand. Collect terms. Example
8. 8. Surds Simplify Rationalise the denominator. Equivalent form Equivalent to multiplying by 1. Example
9. 9. Surds Simplify Equivalent to multiplying by 1. Difference of two squares. Alternate form of the answer. This will rationalise the denominator. Example
10. 10. Surds, Indices and Logarithms Simplify Equivalent to multiplying by 1. Rationalise the denominator. Example
11. 11. Surds, Indices and Logarithms Solve the equation Check Square both sides of the equation. This clears the surds. Example
12. 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. 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. 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. 15. Another rule to apply to the equality of surds Let’s apply this rule to solving an equation. Surds
16. 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