Do Now 4/19/10Do Now 4/19/10 Copy HW in your planner.Copy HW in your planner.

Text p. 655, #4-48 multiples of 4, #56 & 60Text p. 655, #4-48 multiples of 4, #56 & 60

4466

66

A= 16A= 16

A = 4²A = 4²

A= 36A= 36

A = 6²A = 6²

44

What is the area for each figure?What is the area for each figure?

What are the dimensions for each What are the dimensions for each figure?figure?

Write an equation for area of the Write an equation for area of the figure?figure?

Can you think of an equation Can you think of an equation

for ONE side of the figure?for ONE side of the figure?

ObjectiveObjective SWBAT solve quadratic equations by SWBAT solve quadratic equations by

finding square rootsfinding square roots

Remember This???Remember This???Section 2.7 “Find Square Roots and Compare Section 2.7 “Find Square Roots and Compare

Numbers”Numbers”

If If b² = ab² = a then then bb is the is the square rootsquare root of of aa..

TheThe SQUARE ROOTSQUARE ROOT of a number of a number is denoted by the symbol , is denoted by the symbol , which is called awhich is called a radicalradical. .

39 radicandradicand

Square RootsSquare Roots All positive real numbers have two square roots, a positive All positive real numbers have two square roots, a positive

and negative square root. and negative square root.

The symbol is read as “plus or minus” and refers to The symbol is read as “plus or minus” and refers to both the positive and negative square root. both the positive and negative square root.

Negative real numbers do not have real square roots. So Negative real numbers do not have real square roots. So there is no solution.there is no solution.

39

The square of an integer is called a perfect squareperfect square.

100102 81)9( 2

25 no solution

Not PERFECT???Not PERFECT???

The square root of a whole number that is NOT The square root of a whole number that is NOT

a perfect square is an a perfect square is an IRRATIONAL IRRATIONAL NUMBERNUMBER..

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numbers that cannot be written as a quotient (fraction, ratio) of two integers and the decimal neither terminates nor repeats.

To find the square root of a To find the square root of a number that is not a perfect squarenumber that is not a perfect squareestimate or use a calculator to find the estimate or use a calculator to find the square root. square root.

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Section 10.4 “Use Square Roots to Section 10.4 “Use Square Roots to Solve Quadratic Equations”Solve Quadratic Equations”

To use square roots to solve a quadratic equation of To use square roots to solve a quadratic equation of the form the form axax² + bx + c = 0² + bx + c = 0, first isolate , first isolate x²x² on one on one side of the equation to obtain side of the equation to obtain x² = dx² = d. .

Solving xx² = d² = d by Taking Square Roots

- If d > 0, then x² = d has two solutions: dx

0x- If d = 0, then x² = d has one solution:

- If d < 0, then x² = d has no solution: no solution

4

822

2

x

x

0

18182

2

x

x

2x

0x

no solutio

n5

7122

2

x

x

ExamplesExamples

Try It Out…Try It Out…

0252 c

5

25

252

c

c

c

8125 2 a

4

2052

2

a

a

No solution

11112 2 y

0

0

022

2

y

y

y

1442 x

16.3

10

102

x

x

x

Take square roots of a Take square roots of a fractionfraction

In cases where you need to take the In cases where you need to take the square root of a fraction whose square root of a fraction whose numerator and denominator are numerator and denominator are perfect squares, the radical can be perfect squares, the radical can be written as a fraction. written as a fraction.

For example, can be written as For example, can be written as . .

25

165

4

Try It Out…Try It Out…

94 2 c

2

34

9

4

92

c

c

c

21825 2 b

5

425

16

25

16

1625

2

2

b

b

b

b

Solve the quadratic equation. Round Solve the quadratic equation. Round your answer to the nearest hundredth.your answer to the nearest hundredth.

42)4(6 2 x

35.1_;65.6

65.24

74

7)4(

7)4(

2

2

x

x

x

x

x

24)5(3 2 t

17.2_;83.7

83.25

85

8)5(

8)5(

2

2

t

t

t

t

t

HomeworkHomework Text p. 655, #4-48 multiples Text p. 655, #4-48 multiples

of 4, #56 & 60of 4, #56 & 60