Solving Radical Equations

1
Solving Radical Equations
2
A radical equation
is an equation
that contains a radical.
BACK
3
The goal in solving
radical equations
is the same as the goal
in solving most equations.
BACK
4
We need to isolate
the variable.
BACK
5
But there is only one way
to move the variable
out from under the
square root sign.
BACK
6
We need to square the
radical expression.
BACK
7
And, because it is an
equation,
what we do to one side,
BACK
8
And, because it is an
equation,
what we do to one side,
we have to do to the other.
BACK
9
Remember,
no matter what
n is.
(Even if n is an expression)
BACK
10
So we have
BACK
11
(No Transcript)
12
Solve for x
Step 1. Simplify the expression
BACK
13
Solve for x
BACK
14
Solve for x
Step 1. Simplify the expression.
Step 2. Isolate the radical.
BACK
15
Solve for x
BACK
16
Solve for x
Step 1. Simplify the expression.
Step 2. Isolate the radical.
Step 3. Square both sides.
BACK
17
Solve for x
BACK
18
Solve for x
Step 1. Simplify the expression.
Step 2. Isolate the radical.
Step 3. Square both sides.
Step 4. Solve the equation.
BACK
19
Solve for x
BACK
20
Try this one
BACK
21
BACK
22
BACK
23
Try this one
BACK
24
(No Transcript)
25
No Solutions
If you have a square root equaling a negative
number there is no solution.
26
An Extraneous Solution is a solution that does
not satisfy the original equation.
-2 is an extraneous answer.
27
Watch Out!!
If all answers are extraneous, there is also no
solution.
28
(No Transcript)
29
Since -11 does not satisfy the original equation,
11 is the only solution. -11 is an extraneous
solution.
30
Solving Equations with a radical
Solve for a

• 1.) a2 64
• a 8, or -8
• 2.) a2 37
• a 37, or - 37

31
Solving Equations with a radical
Solve for a

• 3.) a2 0
• a 0
• 4.) a2 -25
• No Solution

32
Solving Equations with a radical

• 3x2 - 48 0
• 3x2 - 48 48 0 48
• 3x2 48
• 3x2/3 48/3
• x2 16
• x 16

x ? 4
33
Solving Radical Equations
BACK