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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