7.5 Solving Radical Equations
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.
103 x
25)2( 32
x
103 x
yes
yes
no
EXAMPLE – Solving a Radical Equation0615 x
615 x2
( )2
615 x
3615 x
355 x
7x
Square both sides to get rid of the square root
Let’s Try Some
6232 x 2012)2(4 21
x
RADICAL EQUATIONS02)1n5(3 3
1
2)1n5(3 31
323
1)1n5(
332
33
1)1n5(
278)1n5(
1n5 278 27
2727
8n5 2735n5 27
7n
ISOLATE RADICAL / RATIONAL
RAISE BOTH SIDESTO RECIPROCAL POWER
SOLVE FOR THE VARIABLE
RADICAL EQUATIONS50)2(2 3
2n
250
2)2(2 32
n
25)2( 32
n
23
23
25)2( 32
n
1252 n
1252 n
123127 norn
ISOLATE RADICAL / RATIONAL
RAISE BOTH SIDESTO RECIPROCAL POWER
Use absolute value when taking an evennumber root.
Checking for extraneous solutions
xx 53
53 xx22 )5()3( xx
25103 2 xxx28110 2 xx
)7)(4(0 xx
74 xorx
74 xorxSo check answers with
SOLVING MORE COMPLEX EQUATIONS
0)43()12( 25.05.0 xx25.05.0 )43()12( xx
441
421
])43[(])12[( xx43)12( 2 xx43144 2 xxx
034 2 xx
1,43
x
Raise each side to the 4th power. This will get you integer powers – much easier to work with!
Factor
check for extraneous solutions0)43()12( 25.05.0 xx 1,
43
x