Download Algebra 2 Lesson 7

7.5 Solving Radical Equations
What is a Radical Equation?
• A Radical Equation is
an equation that has
a variable in a
radicand or has a
variable with a
rational exponent.
3  x  10
2
3
yes
( x  2)  25
yes
3  x  10
no
EXAMPLE – Solving a Radical
Equation
5x  1  6  0
5x  1  6
2
2
5 x  1 ( 6 )
5x  1  36
5x  35
x7
Square both sides to get rid of
the square root
Let’s Try Some
2  3x  2  6
1
2
4( x  2)  12  20
RADICAL EQUATIONS
3(5n  1)  2  0
1
3
3(5n  1)  2
1
(5n  1) 3  2 3
1 3
3
(5n  1) 3  2 3 
(5n  1)  8 27 
1
3
5n  8 27   1
5n  8 27   27 27
5n  35 27 
ISOLATE RADICAL / RATIONAL
RAISE BOTH SIDES
TO RECIPROCAL POWER
SOLVE FOR THE VARIABLE
n  7 27 
RADICAL EQUATIONS
2(n  2) 3  50
2
2(n  2) 3 50

2
2
2
ISOLATE RADICAL / RATIONAL
RAISE BOTH SIDES
TO RECIPROCAL POWER
(n  2)  25
2
(n  2)
2
3
3
32
 25
3
2
n  2  125
n  2  125
n  127 or n  123
Use absolute value when taking an even
number root.
Checking for extraneous
solutions
x 3 5  x
x 3  x 5
( x  3 ) 2  ( x  5) 2
x  3  x 2  10 x  25
0  x 2  11x  28
0  ( x  4)( x  7)
x  4 or x  7
So check answers with
x  4 or x  7
SOLVING MORE COMPLEX
EQUATIONS
(2 x  1)
0.5
 (3x  4)
(2 x  1)
0.5
0.25
0
 (3x  4)
1
2 4
0.25
1
4 4
[(2 x  1) ]  [(3x  4) ]
2
(2 x  1)  3x  4
Raise each side to the 4th
power. This will get you
integer powers – much
easier to work with!
4 x 2  4 x  1  3x  4
4x2  x  3  0
3
x  ,1
4
Factor
check for extraneous solutions
(2 x  1)
0.5
 (3x  4)
0.25
0
3
x  ,1
4