Download Solving Radical Equations

Solving Radical Equations
X
The simplest kind of radical
equation is one like this
x 5
To solve it, you need only square
both sides of the equation.
( x )  (5)
2
x  25
2
Of course, most radical equations
are not that simple. Usually there
are several terms on each side.
So the first step in solving a radical equation
is to get it in a form similar to the first
problem we looked at; that is, get the
radical alone on one side of the equation.
Then square both sides of the equation and
solve the resulting equation.
Example
2  2 x  1  34
2 x  1  32
x  1  16
( x  1)  16
2
Divide both sides by 2.
2
x  1  256
x  255
Subtract 2 from each side.
Square both sides
Subtract 1
Let’s practice a few.
Solve:
1.) x  9
2.)2  x  9
3.)3  2 x  9
Check your answers.
Solve
1.) x  9
X=81
2.)2  x  9
X=49
3.)3  2 x  9
X=9
Apply your understanding
Solve
Find a number such that the square root of
3 less than twice the number is equal to 3.
(write the equation and then solve it)
Check your answer.
Write an equation
2x  3  3
2x  3  9
2x  12
x6
Square both sides
Add 3 to both sides
Divide both sides by 2