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Surds
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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
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
Notas del editor
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.