1. 12.3 Solving Radical Equations
Algebra
12.3 Solving Radical Equations

2. Solve 1) √x – 7 = 1 2) √x – 10 = -3 +7 +7 +10 +10 √x = 8 ( )2 ( )2
Let’s Try!!
You Try!!
1) √x – 7 = 1
2) √x – 10 = -3
√x = 8
( )2 ( )2
√x = 7
( )2 ( )2
x = 64
x = 49
Check it!!
Check it!!

3. Isolate the Radical then Solve
Let’s Try!!
You Try!!
3) √2x – = 8
4) √3x + 1 – 2 = 6
√2x – 3 = 5
( )2 ( )2
√3x = 8
( )2 ( )2
2x – 3 = 25
3x + 1 = 64
2x = 28
3x = 63
x = 14
x = 21
Check it!!
Check it!!

4. Checking for Extraneous Solutions
Let’s Try!!
You Try!!
5) √x = x
( )2 ( )2
6) √x + 13 = 2
x + 2 = x2
-x – x – 2
√x = -11
( )2 ( )2
0 = x2 – x – 2
x = 121
0 = (x – 2)(x + 1)
Check it!!
x = 2, -1
Check them!!
121 does not check!
x = 2
-1 does not check!
No solution!

5. Geometric Mean ( )2 ( )2 ( )2 ( )2
The geometric mean of a and b is √ab .
Let’s Try!!
You Try!!
7) The geometric mean of m and 6 is 12.
Find the value of m.
8) The geometric mean of x and 4 is 10.
Find the value of x.
Geometric Mean = √6m
Geometric Mean = √4x
( )2 ( )2
( )2 ( )2
12 = √6m
10 = √4x
144 = 6m
100 = 4x
24 = m
25 = x

6. Try one from the HW Together
P. 725 #35

7. HW
P. 725 #15-53 Odd