Warm Up Simplify each expression. 1. 6 2 36 2. 11 2 121 3. (–9)( – 9) 814. 25 36 Write each...
-
Upload
gwen-washington -
Category
Documents
-
view
213 -
download
0
Transcript of Warm Up Simplify each expression. 1. 6 2 36 2. 11 2 121 3. (–9)( – 9) 814. 25 36 Write each...
![Page 1: Warm Up Simplify each expression. 1. 6 2 36 2. 11 2 121 3. (–9)( – 9) 814. 25 36 Write each fraction as a decimal. 5. 2525 5959 6. 7. 5 3838 8. –1 5656.](https://reader031.fdocuments.us/reader031/viewer/2022032705/56649d875503460f94a6c69d/html5/thumbnails/1.jpg)
Roots and Roots and Irrational Irrational NumbersNumbers
Section 1.5
![Page 2: Warm Up Simplify each expression. 1. 6 2 36 2. 11 2 121 3. (–9)( – 9) 814. 25 36 Write each fraction as a decimal. 5. 2525 5959 6. 7. 5 3838 8. –1 5656.](https://reader031.fdocuments.us/reader031/viewer/2022032705/56649d875503460f94a6c69d/html5/thumbnails/2.jpg)
2.0 Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents.
California Standards
![Page 3: Warm Up Simplify each expression. 1. 6 2 36 2. 11 2 121 3. (–9)( – 9) 814. 25 36 Write each fraction as a decimal. 5. 2525 5959 6. 7. 5 3838 8. –1 5656.](https://reader031.fdocuments.us/reader031/viewer/2022032705/56649d875503460f94a6c69d/html5/thumbnails/3.jpg)
Objectives:
In this lesson you’ll:
• Evaluate expressions containing roots. • Classify numbers within the real number system
![Page 4: Warm Up Simplify each expression. 1. 6 2 36 2. 11 2 121 3. (–9)( – 9) 814. 25 36 Write each fraction as a decimal. 5. 2525 5959 6. 7. 5 3838 8. –1 5656.](https://reader031.fdocuments.us/reader031/viewer/2022032705/56649d875503460f94a6c69d/html5/thumbnails/4.jpg)
Words to know…
• Square root Square root - a number which, when multiplied by itself, produces the given number. (Ex. 7² = 49, 7 is the square
• root of 49)
• Perfect square-Perfect square- any number that has an integer square root.(ex. 100 is a perfect square ,
• Cube root Cube root - a number that is raised to the third power to form a product is a cube root. (ex 23=8, =2)
10100
![Page 5: Warm Up Simplify each expression. 1. 6 2 36 2. 11 2 121 3. (–9)( – 9) 814. 25 36 Write each fraction as a decimal. 5. 2525 5959 6. 7. 5 3838 8. –1 5656.](https://reader031.fdocuments.us/reader031/viewer/2022032705/56649d875503460f94a6c69d/html5/thumbnails/5.jpg)
Square RootsSquares
0² = 0
1² = 1
2² = 4
3² = 9
4² = 16
5² = 25
6² = 36
7² = 49
8² = 64
9² = 81
10² = 100
Perfect Square Roots
00
11 24 39 416
525
636 749
864
![Page 6: Warm Up Simplify each expression. 1. 6 2 36 2. 11 2 121 3. (–9)( – 9) 814. 25 36 Write each fraction as a decimal. 5. 2525 5959 6. 7. 5 3838 8. –1 5656.](https://reader031.fdocuments.us/reader031/viewer/2022032705/56649d875503460f94a6c69d/html5/thumbnails/6.jpg)
Are squares and square roots inverses?
932
2552
8192
39
525
981
A square root is the inverse operation of a square!
![Page 7: Warm Up Simplify each expression. 1. 6 2 36 2. 11 2 121 3. (–9)( – 9) 814. 25 36 Write each fraction as a decimal. 5. 2525 5959 6. 7. 5 3838 8. –1 5656.](https://reader031.fdocuments.us/reader031/viewer/2022032705/56649d875503460f94a6c69d/html5/thumbnails/7.jpg)
Do you know your perfect squares?
1) 49 ?
2) 64 ?
3) 9 ?
5)112 ?
4)52 ?
6)142 ?
7 and -7
8 and -8
3 and -3
25
121
196
![Page 8: Warm Up Simplify each expression. 1. 6 2 36 2. 11 2 121 3. (–9)( – 9) 814. 25 36 Write each fraction as a decimal. 5. 2525 5959 6. 7. 5 3838 8. –1 5656.](https://reader031.fdocuments.us/reader031/viewer/2022032705/56649d875503460f94a6c69d/html5/thumbnails/8.jpg)
Square RootsPositive real numbers have two square roots.
Find the square roots of 16.
The square roots of 16 are 4 and - 4.
4 4 = 42 = 16 = 4 Positive squareroot of 16
(–4)(–4) = (–4)2 = 16 = –4 Negative squareroot of 16
–
![Page 9: Warm Up Simplify each expression. 1. 6 2 36 2. 11 2 121 3. (–9)( – 9) 814. 25 36 Write each fraction as a decimal. 5. 2525 5959 6. 7. 5 3838 8. –1 5656.](https://reader031.fdocuments.us/reader031/viewer/2022032705/56649d875503460f94a6c69d/html5/thumbnails/9.jpg)
Find each root.
Think: What number squared equals 81?
Think: What number squared equals 25?
You try
Think: What number cubed equals –216?
C.
= –6 (–6)(–6)(–6) = 36(–6) = –216
![Page 10: Warm Up Simplify each expression. 1. 6 2 36 2. 11 2 121 3. (–9)( – 9) 814. 25 36 Write each fraction as a decimal. 5. 2525 5959 6. 7. 5 3838 8. –1 5656.](https://reader031.fdocuments.us/reader031/viewer/2022032705/56649d875503460f94a6c69d/html5/thumbnails/10.jpg)
Finding Roots of Fractions.You try
Think: What number squared equals
a.
Think: What number cubed equals
b.
![Page 11: Warm Up Simplify each expression. 1. 6 2 36 2. 11 2 121 3. (–9)( – 9) 814. 25 36 Write each fraction as a decimal. 5. 2525 5959 6. 7. 5 3838 8. –1 5656.](https://reader031.fdocuments.us/reader031/viewer/2022032705/56649d875503460f94a6c69d/html5/thumbnails/11.jpg)
Words to know…• Natural numbers Natural numbers - The counting numbers. (example: 1, 2,
3…)
• Whole numbers Whole numbers - The natural numbers and zero.(example: 0, 1,2,3…)
• Integers Integers -The whole numbers and their opposites.(ex: …-3,-2,-1,0,1,2,3…)
• Rational numbers Rational numbers - Numbers that can be expressed as a fraction (a/b).
![Page 12: Warm Up Simplify each expression. 1. 6 2 36 2. 11 2 121 3. (–9)( – 9) 814. 25 36 Write each fraction as a decimal. 5. 2525 5959 6. 7. 5 3838 8. –1 5656.](https://reader031.fdocuments.us/reader031/viewer/2022032705/56649d875503460f94a6c69d/html5/thumbnails/12.jpg)
Words to know…
• Terminating decimal Terminating decimal -Rational numbers in decimal form that have finite (ends) number of digits. (ex 2/5= 0.40 )
• Repeating decimal Repeating decimal -rational numbers in decimal form that have a block for one or more digits that repeats continuously. (ex. 1.3=1.333333333)
• Irrational numbers Irrational numbers - numbers that cannot be expressed as a fraction including square roots of whole numbers that are not perfect squares and nonterminating decimals that do not repeat.
![Page 13: Warm Up Simplify each expression. 1. 6 2 36 2. 11 2 121 3. (–9)( – 9) 814. 25 36 Write each fraction as a decimal. 5. 2525 5959 6. 7. 5 3838 8. –1 5656.](https://reader031.fdocuments.us/reader031/viewer/2022032705/56649d875503460f94a6c69d/html5/thumbnails/13.jpg)
The real numbers are made up of all rational and irrational numbers.
Note the symbols for the sets of numbers.R: real numbersQ: rational numbersZ: integersW: whole numbersN: natural numbers
Reading Math
![Page 14: Warm Up Simplify each expression. 1. 6 2 36 2. 11 2 121 3. (–9)( – 9) 814. 25 36 Write each fraction as a decimal. 5. 2525 5959 6. 7. 5 3838 8. –1 5656.](https://reader031.fdocuments.us/reader031/viewer/2022032705/56649d875503460f94a6c69d/html5/thumbnails/14.jpg)
Classifying Real Numbers
Write all classifications that apply to each real number.
A.
–32 = –
32 1
rational number, integer, terminating decimal
B.
irrational
–32
–32 can be written in the form .
14 is not a perfect square, so is irrational.
–32 can be written as a terminating decimal.
–32 = –32.0
![Page 15: Warm Up Simplify each expression. 1. 6 2 36 2. 11 2 121 3. (–9)( – 9) 814. 25 36 Write each fraction as a decimal. 5. 2525 5959 6. 7. 5 3838 8. –1 5656.](https://reader031.fdocuments.us/reader031/viewer/2022032705/56649d875503460f94a6c69d/html5/thumbnails/15.jpg)
Write all classifications that apply to each real number.
a. 7
rational number, repeating decimal
Check It Out!
67 9 = 7.444… = 7.4
7 can be written in the form .4 9
can be written as a repeating decimal.
b. –12 –12 can be written in the form .
–12 can be written as a terminating decimal.
rational number, terminating decimal, integer
![Page 16: Warm Up Simplify each expression. 1. 6 2 36 2. 11 2 121 3. (–9)( – 9) 814. 25 36 Write each fraction as a decimal. 5. 2525 5959 6. 7. 5 3838 8. –1 5656.](https://reader031.fdocuments.us/reader031/viewer/2022032705/56649d875503460f94a6c69d/html5/thumbnails/16.jpg)
Write all classifications that apply to each real number.
irrational
100 is a perfect square, so is rational.
10 is not a perfect square, so is irrational.
10 can be written in the form and as a terminating decimal.
natural, rational, terminating decimal, whole, integer
![Page 17: Warm Up Simplify each expression. 1. 6 2 36 2. 11 2 121 3. (–9)( – 9) 814. 25 36 Write each fraction as a decimal. 5. 2525 5959 6. 7. 5 3838 8. –1 5656.](https://reader031.fdocuments.us/reader031/viewer/2022032705/56649d875503460f94a6c69d/html5/thumbnails/17.jpg)
Find each square root.
1. 2.
3. 4.3
5. The area of a square piece of cloth is 68 in2. Estimate to the nearest tenth the side length of the cloth. 8.2 in.
Lesson Quiz
Write all classifications that apply to each real number.
6. –3.89 7.rational, repeating decimal
irrational
15