ROOTS AND POWERS

RACHEL SOPHIA

WILLIAM GUELE

Today’s object

1:review from 4.0-4.6

2:fininsh the worksheet

3:small..small quiz

vocabulary

Welcome Guele

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.

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.

ACROSS2.Any rational or irrational number: Real number4.The number 1 and any other number obtained by adding 1 to it repeatedly: natural number5.An expression consisting of a radical sign, a radicand, and an index: radical6.An integer or a fraction: rational number7.Any of the natural number or zero: whole number

ANSWER KEY

DOWN1.A real number that cannot be expressed as a rational number: irrational number2.The number under a radical sign: radicand3.It is more professional than the whole number: integers

Welcome where I am

Chapter 4.1,4.4,4.5

Roots and ExponentsIrrational Numbers

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.

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

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

Reciprocals§Any two numbers that have a product

of 1 are called reciprocals

§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

When x is any non-zero number and n is a rational number, x-n is the

reciprocal of xn

That is, x-n = 1/xn and 1/x-n = xn, x ≠ 0

Roots and Exponents

Fractional Exponents and Radicals

am*an = am+n

This is exactly the formula what our new concept comes

from.

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!

Sophia’s time

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*

Rational numbers

Irrational numbers

Integers

Whole numbers

National

numbers

Mixed and entire radicals

Question

What will you do if there are too many people in you house?

• Answer is: kick some of them out..

• √16=4*4• √49=7*7• This process is called• multiplication

property of radicals

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)

MathReview Project

Roots and Powers

QUIZ TIME! =w=

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

Roots and Powers

QUIZ TIME

Are You Ready？ START!

100 100 100

200 200 200

300 300 300

QUIZ TIME!

#1.Which of the following statements are true?

A． I and III onlyB. I and IV onlyC. II and III onlyD. II and IV only A

#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 onlyB. II and III onlyC. II, III and IV onlyD. I, II, III and IV

C

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

B

#4. Which pattern could be used to predict 3–4?

A. B.

C. D. A

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

#6. Which of the following number lines best represents the placement of  X, Y, Z, given:

A.

B.

C.

D. A

#7.XX made a mistake in her simplification of  (3a5)/2a4Which step contains her first mistake?A.IB.IIC.IIID.IV

C

#8.Simplify:

A.

B.

C.

D. A

#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.IB.IIC.IIID.IV

B

The Ending of the Class