# High School Math : Solving Radical Equations and Inequalities

## Example Questions

### Example Question #1 : Solving Radical Equations And Inequalities

Solve for :

Explanation:

To solve for  in the equation

Square both sides of the equation

Set the equation equal to  by subtracting the constant  from both sides of the equation.

Factor to find the zeros:

This gives the solutions

.

Verify that these work in the original equation by substituting them in for . This is especially important to do in equations involving radicals to ensure no imaginary numbers (square roots of negative numbers) are created.

### Example Question #2 : Solving Radical Equations And Inequalities

Explanation:

Begin by subtracting  from each side of the equation:

Now, square the equation:

Solve the linear equation:

### Example Question #1 : Solving Radical Equations And Inequalities

Explanation:

Begin by squaring both sides of the equation:

Combine like terms:

Once again, square both sides of the equation:

Solve the linear equation:

### Example Question #3 : Solving Radical Equations And Inequalities

No real solutions

Explanation:

Begin by squaring both sides of the equation:

Now, combine like terms:

Factor the equation:

However, when plugging in the values,  does not work. Therefore, there is only one solution:

### Example Question #1 : Solving Radical Equations And Inequalities

Explanation:

Begin by squaring both sides of the equation:

Now, combine like terms and simplify:

Once again, take the square of both sides of the equation:

Solve the linear equation:

### Example Question #5 : Solving Radical Equations And Inequalities

Explanation:

Begin by taking the square of both sides:

Combine like terms:

Factor the equation and solve:

However, when plugging in the values,  does not work. Therefore, there is only one solution:

### Example Question #4 : Solving Radical Equations And Inequalities

Explanation:

To solve the radical expression, begin by subtracting  from each side of the equation:

Now, square both sides of the equation:

Combine like terms:

Factor the expression and solve:

However, when plugged into the original equation,  does not work because the radical cannot be negative. Therefore, there is only one solution:

### Example Question #1 : Solving Radical Equations And Inequalities

Solve the equation for .

Explanation:

Square both sides.

Isolate .

Solve for :