# Download Lesson 1 - Square Roots - Algebra I Keystone Exam Preparation

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```Name:_________________________________________________________Period:______Date:___________________________
AlgebraIKeystoneExamPreparationProgramoMasteredOn:_____________________
Square Roots
A1.1.1.1.2–Simplifysquareroots(e.g. 24 = 2 6).
LessonPretest
Solvethefollowingproblems.Showyourworkinthespacebelowandfillinthebubblethatrepresentsthe
1.Anexpressionisshownbelow.
21𝑥
Forwhichvalueofxshouldtheexpressionbe
furthersimplified?
A. 5
2.Anexpressionisshownbelow.
2 43𝑥
Which value of 𝑥 makes the expression
equivalentto14 43?
A. 7
B. 6
B. 12
C. 11
C. 49
D. 55
D. 98
1.
2.
A B C D
A B C D
LessonKeywords
Concepts
Square roots are the reverse operation of squaring a value. Numbers whose square roots are Integers are
calledperfectsquares.Forexample: 4 = 2,so4isaperfectsquare.Thesquarerootsymbol(
)iscalled
a radical. You can use a calculator to determine the approximate value of a square root or simplify square
roots,asshownbelow:
CalculatingtheValueofaSquareRoot
Toestimatethevalueofasquareroot,useacalculator.Somecalculatorsrequireyoutoenterthevaluefirst
andthenpressthesquarerootkey(usually % b)andothersrequireyoutopressthesquarerootkeyand
thenenterthevalue.Youwillneedtodeterminewhichmethodyourcalculatoruses.
4.242640687
Solution:Press% bandtype18,thenpresse .
?
TestTakingTip:Useacalculatorthatyouknowhowtouse.Understandhowthefeaturesofthe
calculator work, including how to enter expressions into the calculator. Make sure your
calculatorhasfreshbatteriesandisworkingproperlypriortothedayofthetest.
SimplifyingSquareRoots
Squarerootsthatarenotperfectsquarescansometimesbesimplified.Tosimplifyasquareroot,factorthe
Example2:Simplify 160.
Solution:
STEP1:Factor160insidetheradical: 2 ∙ 2 ∙ 2 ∙ 2 ∙ 2 ∙ 5.
STEP2:Sincetherearetwopairsoftwo,one2fromeachpaircanberemovedfromthe
outside).
STEP3:Repeatthisstepforallpairs,asshown:2 ∙ 2 2 ∙ 5.
The following examples demonstrate two additional methods of determining your understanding of
simplifyingsquareroots.
Example3:Anexpressionisshownbelow.
14𝑥
Forwhichvalueofxshouldtheexpressionbefurthersimplified?
A. 15
B. 23
C. 35
D. 37
Solution:
STEP1:Factorthecoefficientofx,insidetheradical: 2 ∙ 7 ∙ 𝑥.
A. 15 = 3 ∙ 5
B. 23 = 1 ∙ 23(Prime)
C. 35 = 5 ∙ 7
D. 37 = 1 ∙ 37(Prime)
STEP3:ComparethefactorsandmatchthefactorsfromSTEPONEandSTEPTWO.Onlyone
STEP 4: Check your work by replacing 𝑥 with the value you selected and simplifying the
squareroot,asshownbelow.
14𝑥 = 14(35) = 490 = 7 10
Example4:Anexpressionisshownbelow.
2 23𝑥
Whichvalueof𝑥makestheexpressionequivalentto10 23?
A. 5
B. 10
C. 25
D. 50
Solution:
STEP1:Dividethecoefficientoftheequivalentexpressionbythecoefficientoftheoriginal
expression.
10 ÷ 2 = 5
oftheperfectsquare.Therefore,squarethevaluefromSTEPONE.
53 = 25
STEP 3: Check your work by replacing 𝑥 with the value you selected and simplifying the
squareroot,asshownbelow.
2 23𝑥 = 2 23(25) = 2 575 = 10 23
Exercises
A.Estimatethevaluesofthefollowingsquarerootstothenearesttenth.
1. 11
3. 92
5. 14
2. 38
4. 18
6. 56
needed.
7. 24
12. 98
17. 63
8. 10
13. 20
18. 125
9. 32
14. 17
19. 45
10. 18
15. 112
20. 12
11. 54
16. 132
21. 28
C.Findavalueofxthatallowseachexpressiontobefurthersimplified.Donotuseperfectsquares.
22. 22𝑥
26. 110𝑥
23. 35𝑥
27. 60𝑥
24. 42𝑥
28. 33𝑥
25. 30𝑥
29. 70𝑥
D.Findthevalueofxthatmakeseachexpressiontrue.
30.2 14𝑥 = 12 14
34.6 29𝑥 = 12 29
31.3 51𝑥 = 21 51
35.3 22𝑥 = 18 22
32.5 27𝑥 = 25 27
36.2 71𝑥 = 18 71
33.4 33𝑥 = 40 33
37.7 120𝑥 = 42 120
38.Simplifythevalueof 32.Explaineachstep.
LessonPostTest
1.Anexpressionisshownbelow.
55𝑥
Forwhichvalueofxshouldtheexpressionbe
furthersimplified?
A. 7
A. 3
B. 12
B. 9
C. 13
C. 12
D. 15
D. 18
1.
2.
2.Anexpressionisshownbelow.
6 63𝑥
Which value of 𝑥 makes the expression
equivalentto18 63?
A B C D
A B C D
```
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