Name _________________________________________________ Class _______________ Date _______________
Practice
3-1
Perfect Squares, Square Roots, and Equations of the form x2 = p
3-1
Perfect Squares, Square Roots, and Equations of the form
196 .
1.Use the fact that 196 is a perfect square to evaluate
2.Use the fact that 64 is a perfect square to evaluate
64 .
3.Solve the equation z2 = 4. Simplify your answer. Use a comma to separate
answers as needed.
4.Solve the equation y2 = 25 . Simplify your answer. Use a comma to separate
81
answers as needed.
5.Solve the equation v2 = 47. Round to the nearest tenth. Use a comma to
separate answers as needed.
6.The area of a square garden is 1 km2. How long is each side?
81
7.a)Writing Use the fact that 49 is a perfect square to evaluate
b) Describe two situations in which evaluating
49 .
49 would be useful.
8. Error Analysis On a recent homework assignment, Nati needed to solve this
equation completely. He incorrectly wrote “g = –6.”
a) Solve the equation g2 = 36. Simplify your answer. Use a comma to separate
answers as needed.
b) What error did Nati make?
❍❍ A. He did not take the square root of 36 correctly since (–6)2 ! 36.
❍❍ B. He did not solve the equation completely since there is a positive
answer as well.
❍❍ C. He did not square 36 correctly since 362 ! –6.
❍❍ D. He did not solve the equation completely since there are two
negative answers.
9.a)Reasoning Solve the equation w2 = 81 . Simplify your answer. Use a comma
16
to separate answers as needed.
b) If the square of a number is less than 1, does it follow that the number
must be less than 1? If the square of a positive number is greater than 1,
does it follow that the number must be greater than 1? Include examples
to explain your reasoning.
10. Estimation Solve the equation b2 = 77.
a) Estimate using the perfect square closest to 77.
b) Use a calculator. Round to the nearest tenth as needed.
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Practice 3-1
1
Homework G
11. Postage Stamp A square stamp has area 1,120 mm2. About how long is
each side?
12. a) Mental Math Solve the equation c2 = 400. Simplify your answer. Use a
comma to separate answers as needed.
b) Explain how you can use mental math to find the solution.
13. Solve the equation k2 = 1 19 . Simplify your answer. Use a comma to separate
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answers as needed.
14. Challenge Yael used to have a square garage with 228 ft2 of floor space. She
recently built an addition to it. The garage is still a square, but now it has
50% more floor space.
a) What was the length of one side of the garage originally? Round to the
nearest tenth as needed.
b) What is the length of one side of the garage now?
c) What was the percent increase in the length of one side?
15. Challenge Holly wants to make a frame for a painting. The painting is square
and has area 225 square inches. The framing material costs $1.35 per inch.
How much will she spend? You may assume that the framing material Holly
buys will be the exact amount she needs.
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Practice 3-1
2
Homework G
ANSWER
KEY
Practice 3-1: Perfect Squares, Square Roots, and Equations of
the form x2 = p
1.14
2.8
3.2, –2
4. 5 , - 5
9
9
5.6.9, –6.9
6. 1 km
9
7.a)7
b)
Answers will vary
8.a)6, –6
b)
B
9.a) 9 , - 9
4
4
b)
Answers will vary
10. a) 9, –9
b)
8.8, –8.8
11. 33.5 mm
12. a) 20, –20
b)
Answers will vary
13. 1 1 , - 1 1
9
9
14. a) 15.1 ft
b)
18.5 ft
c)
22.5%
15. $81.00
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Practice 3-1
3
Answer Key G