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Page 1: Simplifying Radical Expressions Simplifying Radicals Radicals with variables.

Simplifying Radical Expressions

Simplifying Radicals

Radicals with variables

Page 2: Simplifying Radical Expressions Simplifying Radicals Radicals with variables.

Definition of Square Root: For any real numbers a and b, if a2 = b, then a is a square root of b.

k aIndex number

Radical sign

radicand

Radical Expression

Page 3: Simplifying Radical Expressions Simplifying Radicals Radicals with variables.

Let’s review. Simplify each expression. Assume all values of the variable are positive.

Examples:

543).1( 693

693

633

69

Page 4: Simplifying Radical Expressions Simplifying Radicals Radicals with variables.

Examples:

pp 525 23125).2( p

pp 525 2

pp 55

Page 5: Simplifying Radical Expressions Simplifying Radicals Radicals with variables.

Try these with your partner:

nn 2100

nn 2100

nn10

3100).3( n

Page 6: Simplifying Radical Expressions Simplifying Radicals Radicals with variables.

Try these with your partner:

y5

2

y5

2).4(

y

y

5

5

225

52

y

y

y

y

5

52

Page 7: Simplifying Radical Expressions Simplifying Radicals Radicals with variables.

Adding and Subtracting Radical Expressions

Page 8: Simplifying Radical Expressions Simplifying Radicals Radicals with variables.

Radical expressions can be combined (added or

subtracted) if they are like radicals – that is, they

have the same root ________ and the same

________.

Example 5: and are alike. The root

index is _____ for both expressions and the

radicand is _____ for both expressions.

6 65

index

radicand

2

6

Page 9: Simplifying Radical Expressions Simplifying Radicals Radicals with variables.

Example 6: and are not alike. They

both have the same __________ but the root

_______ are not the same.

To determine whether two radicals are like

radicals, you must first __________ each

radicand.

x4 3 4x

indices

radicand

simplify

Page 10: Simplifying Radical Expressions Simplifying Radicals Radicals with variables.

Simplify each expression:

(7). 6763

(8). 7278

610

76

(9). 215252 29

(10). 5236573

5257363 5935

Page 11: Simplifying Radical Expressions Simplifying Radicals Radicals with variables.

Try these with your partner:

(11). 119112114

(12). 3735 xx

113

32x

(13). 7112976 2975

(14). 133106104139

10101312

106104133139

Page 12: Simplifying Radical Expressions Simplifying Radicals Radicals with variables.

Add or subtract as indicated. Simplify first!

(15). 45457

59457

59457

53457

51257 519

Page 13: Simplifying Radical Expressions Simplifying Radicals Radicals with variables.

(16). 812502

24122252

24122252

224210

214

2212252

Page 14: Simplifying Radical Expressions Simplifying Radicals Radicals with variables.

Try these with your partner:

(17). 1822

2922

25

2922

2322

Page 15: Simplifying Radical Expressions Simplifying Radicals Radicals with variables.

(18). 752274

3252394

32

3252394

352334

310312

Page 16: Simplifying Radical Expressions Simplifying Radicals Radicals with variables.

(19). yy 1092

y4

yy 1092

yy 1092

yy 1032

yy 106

Page 17: Simplifying Radical Expressions Simplifying Radicals Radicals with variables.

(20). xx 207805

x56

xx 5475165

xx 5475165

xx 527545

xx 514520