# Algebra II : Solving and Graphing Radicals

## Example Questions

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### Example Question #1 : Solving Radical Equations

Solve for :

None of the other responses is correct.

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

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 #1 : Solving And Graphing Radicals

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

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:

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:

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:

Explanation:

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

divide both sides by 5

square both sides

### Example Question #8 : Solving Radical Equations

Solve for

Explanation:

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

### Example Question #9 : Solving Radical Equations

Solve for .

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.

Solve for .