Post on 12-Sep-2021
transcript
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