Download Section 9.6

9.6 – Solving Radical Equations
Definitions of the Day (DODs)
• Radical Equation
• Extraneous Solution
 5
 9
 x
2

5 5 
25  5
2

9 9 
81  9
2

x x 
Work Smart, Not Hard!!!
x2  x

Notice that x² is a
perfect square
ax  b

2
 ax  b
Conclusion: Squaring and the
square root undo each other
Definition: Radical Equation
Equations that have the variable
under a radical.
Ex.
10 x  8  14
Definition: Extraneous Solution
Extra solutions introduced when
squaring both sides of an equation.
We must check out answers!!!
Steps to Solve Radical Equations
1) Isolate the radical (get it by itself)
2) Square each side of the equation
3) Solve for the variable.
4) Check for extraneous solutions.
Solve the Equation
1)
x 5 9  3
Solve the Equation
2)
x  5  3x  6
Solve the Equation
3) x  x  6
Your Turn!!
Evaluate
1)
2 x  10  1  6
2)
7x  5  x  3
Sentence Frames
1.
Radical equations are equations that have the variable
under the ________________.
2.
Extraneous solutions are ______________ introduced
by ______________________________________