9.3 Square Roots 9.3 Square Roots Essential Questions: How do you find square roots? How do you estimate square roots?
9.3 Square Roots Essential Questions: How do you find square roots? How do you estimate square roots?
Dec 23, 2015
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9.3 Square Roots9.3 Square Roots
Essential Questions: How do you find square roots?
How do you estimate square roots?
VocabularyVocabulary
• Perfect SquarePerfect Square: A number whose square roots are integers.
• Square RootSquare Root: one of the equal factors that makes up the square.– Uses the “√ ” symbol– Has a positive and negative solution
• Principle Square RootPrinciple Square Root: the positive square root
Squares & Square Roots
• Squares and square roots are inverse operations because they are opposites.
Finding Squares
• List the squares up to 30.12 = 112 = 212 =
22 = 122 = 222 =
32 = 132 = 232 =
42 = 142 = 242 =
52 = 152 = 252 =
62 = 162 = 262 =
72 = 172 = 272 =
82 = 182 = 282 =
92 = 192 = 292 =
102 = 202 = 302 =
Finding Squares
• List the squares up to 30.12 = 1 112 = 121 212 = 441
22 = 4 122 = 144 222 = 484
32 = 9 132 = 169 232 = 529
42 = 16 142 = 196 242 = 576
52 = 25 152 = 225 252 = 625
62 = 36 162 = 256 262 = 676
72 = 49 172 = 289 272 = 729
82 = 64 182 = 324 282 = 784
92 = 81 192 = 361 292 = 841
102 = 100 202 = 400 302 = 900
Finding Square RootsFinding Square Roots
• To find a square root, think backwards from squaring. • “What number times itself makes this number?”
Simplify each root below and identify as a positive root or a negative root.
1) 49
2) 25
3) 144
4) 16
5) 36
6) 36
7) 64
8) 100
7
5
12
4
6
6
8
not a real number
Negative numbers do not have real roots.
positive root
positive root
positive root
positive root
negative root
negative root
negative root
Rational & Irrational
• Rational Roots: real number answers
• Irrational Roots: estimated decimal answers
EstimatingEstimating
• To estimate square roots, find the two roots the number is between.
Determine what two consecutive integers eachirrational root lies between.
1) 7
2) 20
3) 85
4) 45
4 7 9
2 3
lies between 2 and 3
16 20 25
4 5
lies between 4 and 5
81 85 100
9 10
lies between 9 and 10
36 45 49
6 7
lies between 6 and 7
Estimating PracticeEstimating Practice
ApplicationApplication
Summary
• Answer the essential questions in detailed, complete sentences.
• How do you find square roots?• How do you estimate square roots?
• Write 2-4 study questions in the left column to complete the notes.
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