Transcript Solving Radical Equations

Solving Radical
Equations
Steps to Solve
 Isolate
the radical on one side by
moving other terms;
–if there are two radicals, isolate one
radical.
 Raise both sides of the equation to the
power that cancels the radical.
 Solve the remaining equation.
Important!!
 Remember
- what you do to one side of
the equation, you MUST do to the other
side (or else it will get jealous).
 Remember
answers!!
- you MUST check your
Radical Equations
q 80
 Solve:
 Move
the 8:
q 8
 q
2
 Square
both sides:
8
2
q  64
Radical Equations
 Check
your solution:
64  8  0
88 0
00
√
Radical Equations
 Solve:
3
2 p 1  6  3
Radical Equations
3
 Move
 Cube
2 p  1  6  3
the 6:
both sides:
 Solve:
3

3
2p  1  3
2 p  1  3
3
3
2p  1  27
2p  26
p  13
Radical Equations
 Check:
3
2(13)  1  6  3
3
27  6  3
3  6  3
3  3 √
Radical Equations
 This
is also a radical equation:
1
2
x  40

You may want to rewrite the equation with
a radical instead of a rational power:
x  40
Radical Equations

Solve:
x  40
x  4
 x   4
2
x  16
2
Radical Equations

And Check:
16  4  0
44 0
8 0
This does not check - there is no solution!
Radical Equations

This equation has two radicals:
x  x55

Isolate ONE radical:
x 5  5 x

Square both sides [you NEED the ( ) ]:

x5
  5  x 
2
2
Radical Equations

You must FOIL the binomial:
2
2
x  5  5  x 

There is still a radical to be isolated:
x  5  25  10 x  x


x  5  5  x 5  x 
20  10 x
2 x
Radical Equations

Solve the remaining radical equation:
2 x
2   x 
2
2
4x

And check:
4  45 5
23 5 √