Download Algebra Perfect squares and square roots

Name ———————————————————————
SECTION
6
Date ————————————
Algebra
Lesson 3: Perfect Squares and Square Roots
A perfect square is the square of an integer. The square root of a perfect square
is an integer. The table shows how some perfect squares and square roots
are related.
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Ï4 5 2
Square Roots
EXAMPLE 1
32
5333
59
42
5434
5 16
}
}
Ï16 5 4
Ï9 5 3
}
Ï25 5 5
Find the two square roots of 9.
The number 9 has a positive square root and a negative square root.
HINT
The positive square
root and negative
square root of a
number are opposites.
Find a positive number you can square to get 9.
32 5 3 3 3 5 9
Find a negative number you can square to get 9.
(23)2 5 (23) 3 (23) 5 9
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
52
5535
5 25
6. ALGEBRA
3. Squares and Square Roots
22
5232
54
Perfect Squares
So, the two square roots of 9 are 3 and 23.
EXAMPLE 2
}
Evaluate Ï144.
}
The symbol Ï is called a radical sign. It is used to represent
the positive square root.
Find a positive number you can square to get 144.
122 5 12 3 12 5 144
}
Since 122 5 144, Ï144 5 12.
HINT
When you see a
radical sign, find
only the positive
square root.
Practice: First Try
Tell whether the number is a perfect square or not. Write yes or no.
1. 36
2. 48
3. 50
4. 64
5. 72
6. 81
7. 100
8. 125
McDougal Littell Middle School Math
Remediation Book Lesson 6.3
171
Name ———————————————————————
Date ————————————
Practice: Second Try
Find the two square roots of the number.
1. 4
2. 64
3. 100
4. 169
5. 196
6. 900
7. 3600
8. 625
Evaluate the square root.
}
10. Ï 81
}
14. Ï 9
}
18. Ï 121
13. Ï 36
17. Ï 400
}
11. Ï 49
}
12. Ï 16
}
15. Ï 144
}
19. Ï 225
}
}
16. Ï 1
}
}
20.
}
Ï10,000
Extend Your Skills
Approximate each square root to the nearest whole number.
}
}
}
21. Ï 10
22. Ï 65
23. Ï 5
}
24. Ï 40
25. Complete the table. What type of numbers are the areas?
Square
1 in.
2 in.
3 in.
4 in.
5 in.
Side Length (in.)
Area (in.2)
Puzzle
Which number does not belong?
Explain.
172
McDougal Littell Middle School Math
Remediation Book Lesson 6.3
36
124
9
225
16
49
1
4
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
6. ALGEBRA
3. Squares and Square Roots
9. Ï 25
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Name ———————————————————————
SECTION
6
Date ————————————
Algebra
Lesson 3: Perfect Squares and Square Roots
A perfect square is the square of an integer. The square root of a perfect square
is an integer. The table shows how some perfect squares and square roots
are related.
}
Ï4 5 2
Square Roots
EXAMPLE 1
32
5333
59
42
5434
5 16
}
}
Ï16 5 4
Ï9 5 3
}
Ï25 5 5
Find the two square roots of 9.
The number 9 has a positive square root and a negative square root.
HINT
The positive square
root and negative
square root of a
number are opposites.
Find a positive number you can square to get 9.
32 5 3 3 3 5 9
Find a negative number you can square to get 9.
(23)2 5 (23) 3 (23) 5 9
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
52
5535
5 25
6. ALGEBRA
3. Squares and Square Roots
22
5232
54
Perfect Squares
So, the two square roots of 9 are 3 and 23.
EXAMPLE 2
}
Evaluate Ï144.
}
The symbol Ï is called a radical sign. It is used to represent
the positive square root.
Find a positive number you can square to get 144.
122 5 12 3 12 5 144
}
Since 122 5 144, Ï144 5 12.
HINT
When you see a
radical sign, find
only the positive
square root.
Practice: First Try
Tell whether the number is a perfect square or not. Write yes or no.
1. 36
2. 48
3. 50
4. 64
5. 72
6. 81
7. 100
8. 125
McDougal Littell Middle School Math
Remediation Book Lesson 6.3
171
Name ———————————————————————
Date ————————————
Practice: Second Try
Find the two square roots of the number.
1. 4
2. 64
3. 100
4. 169
5. 196
6. 900
7. 3600
8. 625
Evaluate the square root.
}
10. Ï 81
}
14. Ï 9
}
18. Ï 121
13. Ï 36
17. Ï 400
}
11. Ï 49
}
12. Ï 16
}
15. Ï 144
}
19. Ï 225
}
}
16. Ï 1
}
}
20.
}
Ï10,000
Extend Your Skills
Approximate each square root to the nearest whole number.
}
}
}
21. Ï 10
22. Ï 65
23. Ï 5
}
24. Ï 40
25. Complete the table. What type of numbers are the areas?
Square
1 in.
2 in.
3 in.
4 in.
5 in.
Side Length (in.)
Area (in.2)
Puzzle
Which number does not belong?
Explain.
172
McDougal Littell Middle School Math
Remediation Book Lesson 6.3
36
124
9
225
16
49
1
4
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
6. ALGEBRA
3. Squares and Square Roots
9. Ï 25