Solving Radical Equations

Algebra 2 Bell

Ringer:

Check:

xx 2303

222303 xx

xxx 230962

02142 xx

037 xx

0307 xx

37 xx

)7(23037

14304

164

44

)3(23033

6306

366

66

Essential Question:

What is a radical equation and

how do I solve it?

A radical equation is an equation which contains

a radical. The radicand in a radical equation

must contain a variable(s).

is a radical equation

is NOT a radical equation

103x

103 x

Steps for Solving Radical Equations:

1. Isolate the radical on one side of the equation.

2. If the radical is a square root, square each

side of the equation. (If the radical is not a

square root, raise each side to a power equal

to the root index.)

3. Solve the resulting equation.

4. Check your answer(s) to avoid extraneous

roots.

You must check your answers. The

process of squaring the sides of an equation

creates a "derived" equation which may not

be equivalent to the original equation.

Example: -5 = 5

(-5)2 = 52

25 = 25

Consequently, solving this new derived equation

may create solutions that never previously

existed. These "extra" roots that are not true

solutions of the original radical equation are

called extraneous roots and are rejected as

answers.

Example 1: Solve

Solution:

Check:

21 x

22

21 x

41x

5x

215

24

22

Example 2: Solve

Solution:

Check:

0217 x

22

3x

9x

02197

02137

02121

217 x

3x

00

Example 3: Solve

Solution:

Check:

1534 x

124 x

22

124 x

1444 x

36x

153)36(4

153144

15312

1515

Example 4: Solve

Solution:

Check:

No solution

2512 x

312 x

22

312 x

912 x

102 x

5x

251)5(2

25110

259

253

28

Example 5: Solve:

Solution:

Check:

2382 xx

22

2382 xx

2984 xx

189324 xx

x550

x10

21038102

83182

2626

Example 6: Solve

Solution:

Check:

951 xx

22951 xx

95122 xxx

01072 xx

025 xx

0205 xx

25 xx

9)5(515

9254

164

44

9)2(512

9101

11

11

Example 7: Application

The distance d (in nautical miles) that a person

can see to the horizon is given by the formula

where h is the person’s eye level in

feet.

a. If a person’s eye level is 16 feet, how many

nautical miles can the person see to the horizon?

hd 17.1

1617.1d )4)(17.1( 68.4

milesnautical68.4

b. A person can see 5.85 nautical miles to the

horizon. What is the person’s eye level?

hd 17.1

feet25

h17.185.5

h522 )(5 h

h25

Try these :

Example 8: Solve

Solution:

Check:

082 x

82 x

4x

22 4)( x

16x

08162

0842

088

00

Example 9: Solve:

Solution:

Check:

264 x

26420

44 x

22 4)4( x

164 x

20x

2616

264

22

Example 10: For a fire hose with a nozzle that

has a diameter of 2 inches, the flow rate f (in gallons

per minute) can be modeled by

where p is the nozzle pressure in pounds per square

inch.

a. If the nozzle pressure is 9 pounds per square inch,

what is the flow rate in gallons per minute?

pf 120

9120f

3120 f

360f

utepergallons min360

b. If the flow rate is 720 gallons per minute,

what is the nozzle pressure?

pf 120

inchsquareperpounds36

p120720

p622 )(6 p

p36

Example 11: Solve:

Solution:

Check:

xx 2303

222303 xx

xxx 230962

02142 xx

037 xx

0307 xx

37 xx

)7(23037

14304

164

44

)3(23033

6306

366

66

Algebra 2 Bell

Exit Quiz:

10 Points

YOU MUST SHOW ALL WORK

AND CHECK FOR

EXTRANEOUS SOLUTIONS TO

RECEIVE FULL CREDIT.

731 xx