Precalculus : Radical Functions

Study concepts, example questions & explanations for Precalculus

varsity tutors app store varsity tutors android store

Example Questions

Example Question #1 : Solve Radical Equations

Solve for 

Possible Answers:

Correct answer:

Explanation:

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  by dividing by 4:

Example Question #2 : Radical Functions

Solve for 

Possible Answers:

Correct answer:

Explanation:

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 #1 : Radical Functions

Which of the following is a solution to the following equation?

Possible Answers:

Correct answer:

Explanation:

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 is the only option among our choices, we should go with it.

Example Question #4 : Radical Functions

Solve the following radical equation. 

Possible Answers:

Correct answer:

Explanation:

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 #5 : Radical Functions

Solve:

 

Possible Answers:

Correct answer:

Explanation:

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 #6 : Radical Functions

Solve the rational equation: 

Possible Answers:

Correct answer:

Explanation:

Square both sides to eliminate all radicals:

Multiply both sides by 2:

Combine and isolate x:

Example Question #7 : Radical Functions

Solve this radical function:

Possible Answers:

None of these answers.

Correct answer:

Explanation:

Add x to both sides:

Square both sides:

Simplify:

Factor and set equal to zero:

Example Question #8 : Radical Functions

Graph:

Possible Answers:

Varsity3

 

Varsity4

Varsity2

Varsity5

Varsity6

Correct answer:

Varsity2

Explanation:

Remember , for .

Step 1, realize where starts: A) observe  never occurs, B) zero-out the radical component of ;

               

                

                

C) The resulting point is .

Step 2, find simple points for  after

, so use

             

             

             

The next resulting point; .

, so use ;

            

            

            

The next resulting point; .

Step 3, draw a curve through the considered points.

Example Question #71 : Polynomial Functions

Solve for  and use the solution to show where the radical functions intersect:

Possible Answers:

Correct answer:

Explanation:

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  into the function.  

 

The y-coordinate of the intersection point is .

The intersection point of the two radical functions is .

Now graph the two radical functions:

,  

 

 Varsity1

Learning Tools by Varsity Tutors