1. Substituting Surds Slideshow 18 Mathematics Mr SasakiRoom 307

2. Objectives • Substitute surd expressions into algebraic expressions • Rationalise surd denominators when substituting

3. Substitution As we have known for a long time now, substitution is the process of inserting expressions into other expressions. We’ve substituted numerical expressions and algebraic expressions. Today we will substitute surd expressions. The process is similar.

4. Surd Substitution In a simple case, we just need to substitute and then simplify the expression. Example If and , calculate . Try the first worksheet!

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6. Other Cases Let’s recall a few properties about indices. Example If , calculate .

7. Other Cases Let’s try a harder example. Example If and , calculate . Only consider the positive root.

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