Precalculus : Solve radical equations and inequalities
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Example Questions
Example Question #1 : Radical Functions
Solve for 
To solve, first square both sides of the equation to reverse the square-rooting of the binomials, then simplify:
Now solve for 
The x-coordinate for the intersection point is 
Choose one of the two radical functions that compose the equation, and set the function equal to y. The more simple a function is, the easier it is to use:
Now substitute 
The y-coordinate of the intersection point is 
The intersection point of the two radical functions is 
Now graph the two radical functions:
Example Question #1 : Solve Radical Equations And Inequalities
Solve for
In order to solve this equation, we need to isolate the radical. In order to do so, we subtract 3 from both sides which leaves us with:
To get rid of the radical, we square both sides:
the radical is then canceled out leaving us with
We solve for 
Example Question #3 : Radical Functions
Solve for
In order to get rid of the radical, we square both sides:
Since the radical cancels out, we're left with
Subtracting both sides by 1 gives us
We then divide both sides by 6 to get 
Example Question #4 : Radical Functions
Which of the following is a solution to the following equation?
We begin by sqaring both sides of the equation. On the left side, the square root simply disappears, while on the right side we square the term.
We then set the left side equal to 0 by subtracting everything on that side.
We then factor
Therefore,
With problems of this type, it is always wise to double check for any extraneous roots (answers that don't actually work for some reason). However, in this case both answers work. Since
Example Question #5 : Radical Functions
Solve the following radical equation.
When dealing with a radical equation, do the inverse operation to isolate the variable. In this case, the inverse operation of a square root is to square the expression. Thus we square both sides to continue. This yields the following.
Example Question #6 : Radical Functions
Solve:
1) To remove the radicals, raise both sides of the equation to the second power:
2) To remove the radical, raise both side of the equation to the second power:
3) Now simplify, write as a quadratic equation, and solve:
4) Checking for extraneous solutions.
Plugging in
Plugging in
Since the square root of negative 5.4 gives us an imaginary solution we conclude that the only real solution is x=3.
Example Question #7 : Radical Functions
Solve the rational equation:
Square both sides to eliminate all radicals:
Multiply both sides by 2:
Combine and isolate x:
Example Question #8 : Radical Functions
Solve this radical function:
None of these answers.
Add x to both sides:
Square both sides:
Simplify:
Factor and set equal to zero:
Example Question #9 : Radical Functions
Which of the following is and accurate graph of 
Remember 
Step 1, realize where 
C) The resulting point is 
Step 2, find simple points for 
The next resulting point; 
The next resulting point; 
Step 3, draw a curve through the considered points.
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