Solving Radical Equations

The Power Rule Equations Containing One Radical Equations Containing Two Radicals

Definitions A Radical Equation must have at least one

radicand containing a variable

The Power Rule: If we raise two equal quantities to the same power, the

results are also two equal quantities If x = y then xn = yn

Warning: These are NOT equivalent Equations!

2243 xxx

Why are they not Equivalent? Start with a simple original equation: x = 3 Square both sides to get a new equation: x2 = 32 which simplifies to x2 = 9 The only solution to x = 3 is 3 x2 = 9 has two solutions 3 and -3 Raising both sides of the equation to an equal

power is called an irreversible step. Therefore we need to check our solutions to

make sure they are valid.

Equations Containing One Radical To eliminate the radical,

raise both sides to the index of the radical

13

163

43

43

22

x

x

x

x

44

416

4313

:

Check

Sometimes, You First Need to Isolate the Radical Get the radical alone before raising to a power

50:

0)5(

05

1213

113

113

113

2

2

22

andSolutions

xx

xx

xxx

xx

xx

xx

solutiongood

xCheck

discard

xCheck

514

5116

51115

511)5(3

5

02

0110

011)0(3

0

Practice – on the board