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Name ———————————————————————
Lesson
2.1
Date ————————————
Study guide
For use with the lesson “Find Square Roots and Compare Real Numbers”
goal
Find square roots and compare real numbers.
Vocabulary
If b2 5 a then b is a square root of a. All positive real numbers have
two square roots, a positive square root (or principal square root) and
a negative square root.
}
A square root is written with the radical symbol Ï . The number or
expression inside the radical symbol is the radicand.
The square of an integer is called a perfect square.
An irrational number is a number that cannot be written as a quotient
of two integers.
The set of real numbers is the set of all rational and irrational
numbers.
ExamplE 1
Find square roots
Evaluate the expression.
}
a. Ï 400
b.
}
2Ï 16
}
c. 6Ï 81
}
a. Ï 400 5 20
The positive square root of 400 is 20.
The negative square root of 16 is 24.
The positive and negative square roots of 81 are 9 and 29.
}
b. 2Ï 16 5 24
}
c. 6Ï 81 5 69
Exercises for Example 1
Evaluate the expression.
}
1. Ï 289
ExamplE 2
2.
}
2Ï 100
}
3. 6Ï 441
approximate a square root
}
approximate Ï 52 to the nearest integer.
Lesson 2.1
Solution
The greatest perfect square less than 52 is 49. The least perfect square greater
than 52 is 64.
49 < 52 < 64
}
}
}
Ï49 < Ï52 < Ï64
}
7 < Ï 52 < 8
Write a compound inequality that compares 52 to
both 49 and 64.
Take positive square root of each number.
Find square root of each perfect square.
}
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
Solution
}
Because 52 is closer to 49 than to 64, Ï52 is closer to 7 than to 8. So, Ï 52 is
about 7.
2-8
Algebra 1
Chapter Resource Book
CS10_CC_A1_MECR710723_C2L01SG.indd 8
5/10/11 12:54:21 AM
Name ———————————————————————
Lesson
2.1
Date ————————————
Study guide
continued
For use with the lesson “Find Square Roots and Compare Real Numbers”
Exercises for Example 2
approximate the square root to the nearest integer.
}
4. Ï 75
ExamplE 3
5.
}
}
Ï240
6. 2Ï 20
Classify numbers
Tell whether each of the following numbers is a real number, a
rational number, an irrational number, an integer, or a whole
}
}
}
number: Ï64 , Ï 17 , 2Ï 36 .
Number
Real
number?
Rational
number?
Irrational
number?
Integer?
Whole
number?
Yes
Yes
No
Yes
Yes
Yes
No
Yes
No
No
Yes
Yes
No
Yes
No
}
Ï64
}
Ï17
}
2Ï36
graph and order real numbers
}
}
3 }
order the numbers from least to greatest: }
, Ï 16 , 22.2, 2Ï12 , Ï6 .
5
Solution
Begin by graphing the numbers on a number line.
2
24
12
23
3
5
22.2
22
21
0
6
1
2
3
3
}
16
}
4
5
}
Read the numbers from left to right: 2Ï 12 , 22.2, }5, Ï 6 , Ï 16 .
Exercises for Examples 3 and 4
Tell whether each number in the list is a real number, a rational
number, an irrational number, an integer, or a whole number.
Then order the numbers from least to greatest.
}
}
1
7. Ï 10 , 2}, 2Ï 8 , 22, 1.3
2
Lesson 2.1
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
ExamplE 4
}
}
1
8. 2Ï 3 , 2}, 2Ï 11 , 22.5, 4
3
Algebra 1
Chapter Resource Book
CS10_CC_A1_MECR710723_C2L01SG.indd 9
2-9
5/10/11 12:54:22 AM
Answers for Chapter 2
Lesson 2.1 Find Square Roots
and Compare Real Numbers
}
1. 6
3. 3
Î
Î
}
}
1
1
2Ï 19 , }9 , 0.7; rational number: 24.4, }9 , 0.7;
4. 7 5. 22 6. 25
}
rrational number: 2Ï 19 ; integer: none; whole
7. 9 8. 211 9. ±4 10. 9; 16 11. 25; 36
}
Î}19 , 0.7
}
12. 36; 49 13. 2 14. 4 15. 25 16. 27
number: none; 24.4, 2Ï 19 ,
17. 23 18. 8
7
1
15. real number: 2 } , 20.3, 1.15, }; rational
4
4
}
7
1
number: 2 }4 , 20.3, 1.15, }4; irrational number:
}
1
none; integer: none; whole number: none; 2 }4 ,
7
1
20.3, 1.15, }4 16. 7 17. 213 18. }6 19. 218
20. 1.5 ft; 2.5 ft 21. a. 48 in. b. 2 22. 16 in.;
}
19. real number: 25, 2, Ï 9 , Ï 64 ; rational number:
}
}
25, 2, Ï 9 , Ï 64 ; irrational number: none; integer:
}
}
}
}
25, 2, Ï 9 , Ï 64 ; whole number: 2, Ï9 , Ï64 ; 25,
}
}
}
}
2, Ï9 , Ï 64 20. real number: 2Ï16 , 0, Ï 3 , 5.5;
}
rational number: 2Ï16 , 0, 5.5; irrational number:
}
}
}
Ï3 ; integer: 2Ï16 , 0; whole number: 0; 2Ï16 , 0,
}
}
2
}
Ï3 , 5.5 21. real number: 23.6, 2Ï1 , }3, Ï4 ;
2
rational number: 23.6, 2Ï1 , }3 , Ï4 ; irrational
}
}
}
}
number: none; integer: 2Ï1 , Ï 4 ; whole number:
}
}
2
3
}
Ï 4 ; 23.6, 2Ï 1 , }, Ï 4 22. real number: 24,
}
5
5
2Ï 6 , }2, 7; rational number: 24, }2 , 7; irrational
}
number: 2Ï 6 ; integer: 24, 7; whole number: 7;
5
}
24, 2Ï 6 , }2 , 7 23. 5 ft 24. 24 in. 25. about
4.2 knots
1. 69 2. 65 3. 220 4. 25 5. 70 6. 613
7. 25 8. 10 9. 27 10. 12 11. 27 12. 25
}
3 }
13. real number: 2Ï 16 , 3.2, 2}, Ï 9 ; rational
2
}
3 }
number: 2Ï 16 , 3.2, 2}2 , Ï9 ; irrational number:
}
}
}
none; integer: 2Ï 16 , Ï9 ; whole number: Ï9 ;
3
24
}
2Ï16 , 2}2 , Ï9 , 3.2 14. real number: 26, 2}
,
5
24
}
Ï 5 , 2.5; rational number: 26, 2}
, 2.5; irrational
5
}
number: Ï5 ; integer: 26; whole number: none;
24
}
26, 2}
, Ï5 , 2.5
5
15. 18 16. 23.5 17. 245 18. 19 19. 60 ft
20. 2.5 ft
Î
Î
28 in.
Study Guide
1. 17 2. 210 3. 621 4. 9 5. 15 6. 24
}
}
1
7. real number: Ï 10 , 2}, 2Ï 8 , 22, 1.3;
2
1
rational number: 2}2, 22, 1.3; irrational number:
}
}
Ï10 , 2Ï8 ; integer: 22, whole number: none;
1
}
}
21. 36 in. 22. about 7.1 ft
Practice Level C
1. ±30 2. 260 3. 14 4. 26 5. ±18 6. 222
7. 7 8. 215 9. 19 10. 212 11. 17 12. 221
}
2Ï8 , 22, 2}2, 1.3, Ï10 8. real number: 2Ï 3 ,
1
1
}
2}3 , 2Ï 11 , 22.5, 4; rational number: 2}3 , 22.5,
}
}
4; irrational number: 2Ï 3 , 2Ï 11 ; integer: 4,
}
Practice Level B
}
Î
}
}
A10
}
}
2
2. 10
15
}
2Ï 169 , 2}
, Ï 6 , 7.25 14. real number: 24.4,
2
Practice Level A
2
}
Ï6 ; integer: 2Ï169 ; whole number: none;
1. 11 feet 2. yes 3. 72 inches left over
2
}
15 }
13. real number: 2Ï 169 , 2}, Ï 6 , 7.25; rational
2
}
15
}
number: 2Ï 169 , 2 2 , 7.25; irrational number:
}
1
whole number: 4; 2Ï11 , 22.5, 2Ï 3 , 2}3, 4
Challenge Practice
1. 2, 8, 18, 32, 50, 72, 98 2. 3, 12, 27, 48, 75
3. 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 4. 5, 20,
45, 80 5. 6, 24, 54, 96 6. 7, 28, 63 7. 4, 64
8. 9 9. 1, 16, 81 10. 25 11. 36 12. 49
Lesson 2.2 Solve One-Step
Equations
Teaching Guide
Alternative Lesson Starter: 1.75r 5 525; 300 mi/h;
divide each side by 1.75.
Practice Level A
1. Subtract 23. 2. Add 218. 3. Subtract 250.
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
answers
Teaching Guide
Solving Linear Equations
4. yes 5. no 6. yes 7. x 5 8 8. n 5 5
9. w 5 11 10. y 5 19 11. a 5 12
3
1
1
2
12. m 5 14 13. 5; } 14. }; 4 15. 2}; 2}
5
4
2
3
Algebra 1
Chapter Resource Book
CS10_CC_A1_MECR710723_C2AK.indd 10
5/21/11 1:53:15 AM