# Algebra II : Solving Radical Equations

## Example Questions

### Example Question #21 : Solving Radical Equations

Solve and simplify:

Explanation:

To solve for x, first we must isolate the radical on one side:

Next, square both sides to eliminate the radical:

Now, take the cube root of each side to find x:

Finally, factor the term inside the cube root and see if any cubes can be pulled out of the radical:

### Example Question #22 : Solving Radical Equations

Solve:

Explanation:

Subtract 14 on both sides.

Simplify both sides.

To eliminate the radical, square both sides.

Simplify both sides.

Divide by two on both sides.

### Example Question #23 : Solving Radical Equations

Solve the equation:

Explanation:

Subtract  from both sides to group the radicals.

Square both sides.

Use the FOIL method to simplify the right side.

Combine like-terms.

Subtract one from both sides, and add  on both sides.

The equation becomes:

Divide by two on both sides and distribute the terms inside the radical.

Square both sides.

Simplify the right side by FOIL method.

Subtract  on both sides.  This is the same as subtracting  on both sides.

Subtract  on both sides.  The equation will become:

Multiply by four on both sides to eliminate the fractional denominator.

Use the quadratic equation to solve for the roots.

Substitute the values of  and  back into the original equation, and only  will satisfy both sides of the equation.

### Example Question #24 : Solving Radical Equations

Solve, and ensure there are no radicals in the denominator

None of these

Explanation:

### Example Question #25 : Solving Radical Equations

Solve the equation:

Explanation:

Square both sides.

Use the FOIL method to expand the right side.

Subtract  from both sides.  The equation becomes:

Use the quadratic equation to determine the roots.

Reduce the fraction.

### Example Question #26 : Solving Radical Equations

Solve:

Explanation:

Simplify both sides of the equation.

Square both sides.

Divide both sides by three.

### Example Question #27 : Solving Radical Equations

Solve:

Explanation:

To isolate the x-variable, first subtract three from both sides.

Square both sides.

The equation becomes:

Subtract two from both sides.

Divide by three on both sides.

### Example Question #28 : Solving Radical Equations

Solve:

Explanation:

Notice that the range of the parent function  must be greater than zero.  There will be no values of square root  that will equal to negative two.

### Example Question #29 : Solving Radical Equations

Solve the equation:

Explanation:

In order to eliminate the radicals, simply square both sides.

The equation becomes:

Simplify the right side by distribution.

Subtract  from both sides.  The equation becomes:

Add 2 on both sides and simplify both sides.

### Example Question #30 : Solving Radical Equations

Solve the equation:

Explanation:

Divide by two on both sides.

The equation becomes:

Square both sides.