11.3

Solving Radical Equations

11.3 – Solving Radical Equations

Goals / “I can…”Solve equations containing radicalsIdentify extraneous solutions

Inverse OperationsHow would you solve the following

equation?

Solve by taking the SQUARE ROOT. Why?

Square roots and Squaring are inverse operations… they “undo” eachother!

2 9x

11.3 – Solving Radical Equations

Inverse OperationsSo… consider this: How could you solve

for x now?

Solve by doing the inverse operation: SQUARING!

4x

2 2

4x

16x

11.3 – Solving Radical Equations

A Refresher on Inverses (opposites):

Opposite of Multiply is ____________Opposite of Add is ____________Opposite of Divide is ____________Opposite of Subtract is ____________Opposite of squaring is ____________Opposite of square rooting is ____________

11.3 – Solving Radical Equations

11.3 – Solving Radical Equations

A radical equation is an equation with a radical in it.

204 x

11.3 – Solving Radical Equations

Try

306 x

Steps to Solving Radical Eq.’sSteps to Solving Radical Eq.’sIsolate the radicand – get all

radicands on one side and all constants on the other.

Square both sides of the equationSolve for xCHECK YOUR ANSWER!!!!

11.3 – Solving Radical Equations

11.3 – Solving Radical Equations

If there are square roots on both sides, square both sides to get rid of them.

6543 xx

#1 Solve xx 42

2242 xx

28162 xxx 29140 xx

1490 2 xx

)2)(7(0 xx

2 ,7x

Standard Form

11.3 – Solving Radical Equations

Check

7x 2x

7427

39

33

7x

xx 42

2422

24

22

2x

11.3 – Solving Radical Equations

#2 Solution

22

2 555 x

2555 2 x

0205 2 x

2x

555 2 x

0)4(5 2 x

0)2)(2(5 xx

Standard Form

11.3 – Solving Radical Equations

Check2x 2x

555 2 x

55)2(5 2

55)4(5

525

2x

55)2(5 2

55)4(5

525

2x

11.3 – Solving Radical Equations

11.3 – Solving Radical Equations

An extraneous solution is a solution that does not make the original problem true.

11.3 – Solving Radical Equations

Example:

xx 12

11.3 – Solving Radical Equations

Sometimes an equation has no solution.

You can only know this by putting the solution into the original equation.

283 x

11.3 – Solving Radical Equations

Solve:

x = x + 6

11.3 – Solving Radical Equations

Solve

2x + 6 = 4