7.3 Binomial Radical Expressions

Review Example

521

2

az8

z5

5

22

1

az8

z5

521az8

5

5 342

5 342

az2

az2

5 555

5 34

az2

az20

az2

az205 34

RADICAL EXPRESSIONSEX-adding

• RULES– Have to have

same number on inside

– Have to have same nth root

482273122

3162393342

342333322

383934

321

RADICAL EXPRESSIONSEX-adding

333 128544163

3 73 33 4 223423

3 63 33 3 22234223

3233 22234223

333 2421226 3 22

Let’s try some . . .

7238418

3 832350

Solutions

7238418

3 832350

Review - RATIONALIZING a DENOMINATOR

• How to rationalize using conjugates– If there is a radical in the bottom, then you

must rationalize it.

2

5

2

2

2

25

How to rationalize when there are rationals in the denominator…

32a2

53 2

3 2

a2

a2

3 33

3

a2

a20

a2

a203

Multiply by the same root but make it so youcan take root of the powers

Let’s remember conjugates

?)5 (2 of conjugate theisWhat )52(

)342(

44484

Sample: Find the conjugate of

Multiply the binomial by the conjugate using the box method.

2

4

16(3)=-48)34

34 2

)38

)38

Notice: No roots appear in our solution when we multiply by a conjugate

RADICAL EXPRESSIONS EX-FOIL Method

)32)(3253(

56 153 34 6+ - -

Fully simplified since radicals can’t break downand our addition rules don’t apply

EX-rationalizing

35

31

35

35

3353525

33535

22

368

11

334

CONJUGATE