1. Simplifying Surds Slideshow 6, Mr Richard Sasaki, Room 307

2. Objectives Understand the meaning of rational numbersUnderstand the meaning of rational numbers Understand the meaning of surdUnderstand the meaning of surd Be able to check whether a number is a surd or notBe able to check whether a number is a surd or not Be able to simplify surdsBe able to simplify surds

3. Rationality First we need to understand the meaning of rational numbers. What is a rational number? A rational number is a number that can be written in the form of a fraction.

4. Rationality If a number is not rational, we say that it is. irrational Example

5. Answers – Questions 1 - 4

6. Answers – Questions 5 - 6

7. Surds What is a surd? A surd is an irrational root of an integer. We can’t remove its root symbol by simplifying it. Are the following surds? Yes! No! Yes! Yes! Even if the expression is not fully simplified, if it is a root and irrational, it is a surd.

8. Multiplying Roots How do we multiply square roots? If we square both sides, we get… If we square root both sides, we get…

9. Simplifying Surds Example We try to take remove square factors out and simplify them by removing their square root symbol.

10. Answers - Easy Square numbers.

11. Answers – Hard (Questions 1 – 3)

12. Answers – Hard (Questions 4 – 5) 92 ② 46 ② 23 288 ② 144 ② 72 ② 36 ② 18 ② 9 ③ ③ 1875 ③ 625 ⑤ 125 ⑤ 25 ⑤ ⑤