# Algebra II : Solving Radical Equations

## 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 #3 : Solving Radical Equations

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 :

or

no solution

or

or

or

Explanation:

To solve, first square both sides:

squaring the left side just givs x - 3. To square the left side, use the distributite property and multiply :

This is a quadratic, we just need to combine like terms and get it equal to 0

now we can solve using the quadratic formula:

This gives us 2 potential answers:

and

### Example Question #9 : Solving Radical Equations

Solve for :

or

or

or

Explanation:

If we consider a quadratic equation one where , this is a quadratic with . We can re-write it so that it is set equal to 0, and then we can use the quadratic formula or a different method to solve:

or in terms of ,

Putting this into the quadratic formula, we get

This gives us 2 answers, and

Remembering that these are potential answers for u, we can finish solving:

square both sides

and

square both sides

Solve for