Algebra 2 Lesson 7
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Transcript 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
x7
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
1
2 4
0.25
0
(3x 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