# Algebra II : Solving and Graphing Radicals

## Example Questions

### Example Question #61 : Solving And Graphing Radicals

Solve:

Explanation:

Square both sides.

We will need to simplify the left side using the FOIL method.

The expression becomes:

Combine like-terms and rewrite the equation.

Isolate the radical by adding  and subtract 17 on both sides.  Then divide by two on both sides.

The radicals can be combined as one whole using the FOIL method.

Square both sides.

The  terms will cancel by subtracting the term on both side, and we can solve for .

Multiply by four on both sides to eliminate the fraction.

Solve for x.

### Example Question #62 : Solving And Graphing Radicals

Solve:

Explanation:

Divide by four on both sides.

The equation becomes:

Square both sides.

Divide by three on both sides.

### Example Question #63 : Solving And Graphing Radicals

Solve:

Explanation:

Multiply by  on both sides.

Simplify both sides.

Square both sides to eliminate the radical.

Simplify both sides.

Divide by  on both sides.

### Example Question #64 : Solving And Graphing Radicals

Explanation:

Divide by two on both sides.  This is similar to multiplying by one-half.

Simplify both sides.

Cube both sides to eliminate the radical.

Divide by three on both sides.  This is similar to multiplying by one-third on both sides.

### Example Question #65 : Solving And Graphing Radicals

Solve the equation:

Explanation:

Subtract 31 from both sides of the equation.

Square both sides.

Simplify both sides.

### Example Question #66 : Solving And Graphing Radicals

Solve the equation:

Explanation:

To eliminate the radical, we will have to cube both sides.

The equation becomes:

Divide by three on both sides.

### Example Question #67 : Solving And Graphing Radicals

Solve:

Explanation:

Divide by three on both sides.

Rewrite the equation.

Raise both sides to the fourth power.

Simplify both sides.

Multiply by 81 on both sides to eliminate the fraction.

Subtract 729 from both sides.

Divide by negative 162 on both sides.

Reduce the fractions.  Double negatives will negate, turning the answer positive.

### Example Question #68 : Solving And Graphing Radicals

Evaluate:

Explanation:

Divide by three on both sides.  The equation becomes:

Raise both sides by four.

Subtract four on both sides.

Divide by negative two on both sides.

### Example Question #69 : Solving And Graphing Radicals

Solve the equation:

Explanation:

Multiply by six on both sides of the equation.

The equation becomes:

Cube both sides to eliminate the radical.

Divide by five on both sides.

Explanation: