simplifying radical expressions simplifying radicals radicals with variables

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

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

Examples:

543).1( 693

693

633

69

Examples:

pp 525 23125).2( p

pp 525 2

pp 55

Try these with your partner:

nn 2100

nn 2100

nn10

3100).3( n

Try these with your partner:

y5

2

y5

2).4(

y

y

5

5

225

52

y

y

y

y

5

52

Adding and Subtracting Radical Expressions

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

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

Simplify each expression:

(7). 6763

(8). 7278

610

76

(9). 215252 29

(10). 5236573

5257363 5935

Try these with your partner:

(11). 119112114

(12). 3735 xx

113

32x

(13). 7112976 2975

(14). 133106104139

10101312

106104133139

Add or subtract as indicated. Simplify first!

(15). 45457

59457

59457

53457

51257 519

(16). 812502

24122252

24122252

224210

214

2212252

Try these with your partner:

(17). 1822

2922

25

2922

2322

(18). 752274

3252394

32

3252394

352334

310312

(19). yy 1092

y4

yy 1092

yy 1092

yy 1032

yy 106

(20). xx 207805

x56

xx 5475165

xx 5475165

xx 527545

xx 514520