Algebra II : Solving and Graphing Radicals

Study concepts, example questions & explanations for Algebra II

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Example Questions

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Example Question #1 : Solving Radical Equations

Solve for :

Possible Answers:

None of the other responses is correct.

Correct answer:

None of the other responses is correct.

Explanation:

One way to solve this equation is to substitute  for  and, subsequently,  for :

Solve the resulting quadratic equation by factoring the expression:

Set each linear binomial to sero and solve:

or 

 

Substitute back:

 - this is not possible.

 

 - this is the only solution.

 

None of the responses state that  is the only solution.

 

 

Example Question #2 : Solving Radical Equations

Solve the following radical equation.

Possible Answers:

Correct answer:

Explanation:

We can simplify the fraction:

Plugging this into the equation leaves us with:

 

Note: Because they are like terms, we can add them.

 

Example Question #3 : Solving Radical Equations

Solve the following radical equation. 

Possible Answers:

Correct answer:

Explanation:

In order to solve this equation, we need to know that

             

How? Because of these two facts: 

  1. Power rule of exponents: when we raise a power to a power, we need to mulitply the exponents:

                                      

 

With this in mind, we can solve the equation:

In order to eliminate the radical, we have to square it. What we do on one side, we must do on the other.

 

Example Question #4 : Solving Radical Equations

Solve the following radical equation.

Possible Answers:

Correct answer:

Explanation:

In order to solve this equation, we need to know that 

 

Note: This is due to the power rule of exponents.

With this in mind, we can solve the equation:

In order to get rid of the radical we square it. Remember what we do on one side, we must do on the other.

Example Question #5 : Solving Radical Equations

Solve for x:

Possible Answers:

Correct answer:

Explanation:

To solve, perform inverse opperations, keeping in mind order of opperations:

first, square both sides

subtract 1

divide by 2 

 

Example Question #6 : Solving Radical Equations

Solve for x:

Possible Answers:

Correct answer:

Explanation:

To solve, perform inverse opperations, keeping in mind order of opperations:

take the square root of both sides

subtract 19 from both sides

square both sides

 

Example Question #7 : Solving Radical Equations

Solve for x:

Possible Answers:

Correct answer:

Explanation:

To solve, use inverse opperations keeping in mind order of opperations:

divide both sides by 5

square both sides

add 12 to both sides

Example Question #8 : Solving Radical Equations

Solve for 

Possible Answers:

Correct answer:

Explanation:

 To get rid of the radical, we square both sides.

Example Question #9 : Solving Radical Equations

Solve for .

Possible Answers:

No answer

Correct answer:

No answer

Explanation:

To get rid of the radical, we need to square both sides. The issue is radicals don't generate negative numbers unless we talk about imaginary numbers. In this case, our answer choice should be no answer. 

Example Question #10 : Solving Radical Equations

Solve for .

Possible Answers:

Correct answer:

Explanation:

 Square both sides to get rid of the radical.

 Subtract  on both sides.

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