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# ROOTS AND POWERS

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1. ROOTS AND POWERS RACHEL SOPHIA WILLIAM GUELE

2. Today’s object 1:review from 4.0-4.6 2:fininsh the worksheet 3:small..small quiz

3. vocabulary Welcome Guele

4. Down 1.A real number that cannot be expressed as a rational number. 2.The number under a radical sign. 3.It is more professional than the whole number. Across 2.Any rational or irrational number. 4.The number 1 and any other number obtained by adding 1 to it repeatedly. 5.An expression consisting of a radical sign, a radicand, and an index. 6.An integer or a fraction. 7.Any of the natural number or zero.

5. ANSWER KEY ACROSS 2.Any rational or irrational number: Real number 4.The number 1 and any other number obtained by adding 1 to it repeatedly: natural number 5.An expression consisting of a radical sign, a radicand, and an index: radical 6.An integer or a fraction: rational number 7.Any of the natural number or zero: whole number

6. DOWN 1.A real number that cannot be expressed as a rational number: irrational number 2.The number under a radical sign: radicand 3.It is more professional than the whole number: integers

7. Welcome where I am Chapter 4.1,4.4,4.5

8. Roots and Exponents Irrational Numbers

9. Irrational Numbers §Numbers that can be written in the form of a fraction or ratio,or more specifically as a quotient of integers are RATIONAL NUMBERS. §Any number that cannot be written as a quotient of integers is called an IRRATIONAL NUMBER. §πis one example of an irrational number.

10. Give me more examples of IRRATIONAL numbers. √2, √3, √5, √0.24, √0.5, 3√-5 Give me more examples of RATIONAL numbers. √100, √0.25, 3√8, 0.5, 5/6, 7, 5√-32

11. Review Time §Written as a decimal number, rational numbers either: • Repeat • Terminate §Rational numbers can be written as a quotient of integers §Written as a decimal number, irrational numbers neither repeat or terminate §Irrational numbers cannot be written as a quotient of integers §All rational and irrational numbers are included in the set of real numbers

12. Reciprocals §Any two numbers that have a product of 1 are calledreciprocals §Using the exponent law: am x an = am+n, we can see that this rule also applies to powers §Since the product of these two powers is 1, 5-2 and 52 are reciprocals

13. When x is any non-zero number and n is a rational number, x-n is the reciprocal of xnThat is, x-n = 1/xn and 1/x-n = xn, x ≠ 0

14. Roots and Exponents Fractional Exponents and Radicals

15. am*an = am+n This is exactly the formula what our new concept comes from.

16. The Equation • The equivalent expression: • √5 =52/1 The new formula: A(m/n)=n√Am More formula will talk later in LAWS of EXPONENTS!

17. Sophia’s time

18. The word’s family • The society-—real numbers: any type of number is belong to society. • The grandparents---rational numbers: can be write in m/n. • The parents---integers: -3,-2,-1,0,1,2,3 • You---whole numbers:0,1,2,3*no negative* • Your future baby-- natural numbers: • 1,2,3*no 0*

19. Rational numbers Integers Irrational numbers Whole numbers National numbers

20. Mixed and entire radicals

21. Question What will you do if there are too many people in you house? What will you do if you feel lonely since only one person stay in your house? Answer is: invite somebody. 7√3=√147 The number such as 7√3 Is called(mixed radicals) • Answer is: kick some of them out.. • √16=4*4 • √49=7*7 • This process is called • multiplication property of radicals

22. Math QUIZ TIME! =w= Roots and Powers Review Project

23. QUIZ TIME - RULES #1. You will be divided into 6 groups, each row is a group, if you answer a question correctly you will get the corresponding point,the team with the highest mark will win a big prize. #2. You have only 30seconds to answer these question

24. Roots and Powers QUIZ TIME Are You Ready？ START!

25. QUIZ TIME! 100 100 100 200 200 200 300 300 300

26. #1.Which of the following statements are true? A．I and III only B. I and IV only C. II and III only D. II and IV only A

27. #2. Which of the following statements are true? I.The factors of 24 are 2, 3, 4, 6, 8 and 12. II.The prime factorization of 24 is 23 × 31 III.The prime factors of 24 are 2 and 3. IV.24 is an irrational number. A．I and IV only B. II and III only C. II, III and IV only D. I, II, III and IV C

28. #3. Simplify: √72 A. √ 26 B. √ 62 C. 18 √ 2 D. 36 √ 2 B

29. #4. Which pattern could be used to predict 3–4? A. B. C. D. A

30. #5.Evaluate: A.-8 B.1/8 C.1/2 D.2 B

31. #6. Which of the following number lines best represents the placement of  X, Y, Z, given: A. B. C. D. A

32. #7.XX made a mistake in her simplification of  (3a5)/2a4 Which step contains her first mistake? A.I B.II C.III D.IV C

33. #8.Simplify: A. B. C. D. A

34. #9.A research assistant calculated the brain mass, b, of an 8 kg cat. She used the formula, where m is the total mass of the cat. In which step did the research assistant first make a mistake? A.I B.II C.III D.IV B

35. The Ending of the Class