Download Example 1 Solving Radical Equations Algebraically

Radical Equation
Equation with a variable under radical sign
Steps for Solving Radical Equation Steps:
Reminder: Radicals are the same as exponents in PEMDAS order
[1] Isolate the radical term: “Cancel all outside operations”
[2] Remove Radical Sign by Powering both sides by Root
Square for
...  #
Cube for 3
...  #
Fourth for
4
...  #
[3] SOLVE remaining equation and
check for Extraneous Solution
Extra solutions that do not satisfy original
Extraneous Solutions: equation because of the domain for radicals
Example 1
[1]
Solving Radical Equations Algebraically
x 1  2  4
[2]
y  2 1  5
y2 6
y  2  36
y  38
[3]
x
5 2 4
3
[4]
7 y
 7  10
3
Example 1: continued
[5]
x  1  5  15
x  1  10
x  1  100
x  101
[7]
4b  1  3  0
[6]
y  3 1  7
y 3 8
y  3  64
y  61
[8] 4  3 x  2  2
Example 1: continued
[9]
5x  2  2 7
[10]
x 7  3 x
[11]
b
6  3 5
3
[12]
2x  4  3  5x
Radicals CW: Solve Algebraically
1.
x  5  12  4
x  6  10  4
2.
x  6  14
x  6  196
x  190
x  5  16
x  5  256
x  251
3.
2 x  2  11  17
2x  2  6
2 x  2  36
2 x  38
x  19
4.
3 5 x  1  11  17
3 5x  1  6
5x  1  2
5x  1  4
5x  5
x 1
5.
4 2x  1  5  9
6.
7 4 x  1  14
4 2x  1  4
2x  1  1
2x  1  1
2x  0
x0
7.
x
3 6   15
2
7 4 x  1  2  16
4x  1  2
4x  1  4
4x  3
3
x
4
8.
2x  5
4
 2  26
3
Example 2
Solving Radical Equations with Multiple Variables
[1]
xa b
[2]
[3]
3 pq  r
[4]
rs  t
2p q a  7
Example 3
[A]
Solving Graphically
3x  1  5 x  1
[B]
2x  3  3  2x
x=½
Example 3
[C]
Continued
y  21 1  y  12
Y=4
[D]
x  1  x  6 1
x=3
Example 4
[A]
No Solutions
x  15  3  x
[B]
3x  2  x  4
x=Ø
Example 5
[A]
Misc. Equations
4  x  x2  8
[B]
3x  7  x  3
x = -1, -2
x=3