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