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.