# Algebra II : Solving Radical Equations

## Example Questions

### Example Question #101 : Solving Radical Equations

Solve the radical equation:

Explanation:

Multiply the radical denominator on both sides.

The equation becomes:

Divide by two on both sides.

Raise both sides by the power of four to eliminate the radical.

Divide by four on both sides.  This is the same as multiplying one-fourth on both sides.

### Example Question #102 : Solving Radical Equations

Solve:

Explanation:

Multiply the denominator on both sides to eliminate the denominator.

Square both sides.

Divide by four on both sides.

### Example Question #103 : Solving Radical Equations

Solve the equation:

Explanation:

Square both sides of the radical to eliminate the square root.

The equation becomes:

Add 9 on both sides.

Divide by 5 on both sides.

### Example Question #104 : Solving Radical Equations

Evaluate:

Explanation:

Divide terms of the radicals on the left side.

### Example Question #105 : Solving Radical Equations

Solve the equation:

Explanation:

Multiply by negative three on both sides.

Square both sides.

Add three on both sides.

Divide by negative seven on both sides.

### Example Question #106 : Solving Radical Equations

Solve the equation:

Explanation:

Multiply the denominator on both sides to eliminate the fraction.

The equation becomes:

Square both sides.

Divide by 500 on both sides.

Reduce both fractions.

### Example Question #107 : Solving Radical Equations

Solve:

Explanation:

Add 5 on both sides.  This is the same as adding  on both sides.

To eliminate the radical, we must square both sides of the equation.

### Example Question #108 : Solving Radical Equations

Solve:

Explanation:

Multiply the denominator on both sides to eliminate the denominator.

Simplify both sides.

Subtract 12 from both sides.

The equation becomes:

Divide by 4 on both sides.

Raise both sides by the power of four to eliminate the radical.

Multiply by one half on both sides to isolate .

### Example Question #109 : Solving Radical Equations

Solve:

Explanation:

Subtract five from both sides of the equation.

Divide by negative three on both sides.

Square both sides.

Simplify both sides.

Multiply by one-ninth on both sides.

### Example Question #110 : Solving Radical Equations

Solve the equation:

Explanation:

Cross multiply both sides.

Square both sides in order to cancel the radicals.

Divide by 2 on both sides.

Square root both sides.

Only  will satisfy the original equation.