11.1 Simplifying Radical Expressions

3

2

1Definitions

Simplifying Radicals

Practice Problems

2

Definitions

3

Perfect Squares

244

399

86464

74949

63636

52525

41616

98181

10100100

11121121

13169169

12144144

4

How a Square Root Works

4222

5

Simplifying Square Roots

Steps Factor the radicand into the product of the

largest factor that is a perfect square Separate the square root into 2 separate

square roots Solve the perfect square Check to make sure you can’t factor the

radicand by another perfect square

6

Simplifying a Square Root Example

12

34

34

32

90

109

109

103

7

Multiplying Square Roots

Steps Multiply the real numbers & leave outside

the square root Multiply the radicands to each other &

leave inside the square root Simplify the square root if possible

8

Multiplying a Square Root Example

153

45

59

59

53

153

9

Multiplying a Square Root Example

6234

6324

188

298

298

238

224

10

Simplifying a Square Root with Variables

Steps Rewrite the variable as a square using the

exponent rules Squares (2nd power) will cancel with square

roots

11

Square Root Variable Example

12x

26 )(x

6x

3y

yy 2

yy 2

yy

12

Putting It All Together

35440 zyx

35440 zyx

zzyyx 242 2

)(104

zzyyx 2222 )()(1042

13

Putting It All Together (Cont.)

zzyyx 2222 )()(1042

zzyyx 22102

yzzyx 102 22

14

Practice Problems

Page 589-590Problems 4-8, 14-25

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