Radical equations are equations that involve radical expressions. They can be solved by isolating the variable and applying the appropriate operations to both sides of the equation. Let's take a look at the step-by-step process for solving radical equations.

Step 1: Isolate the radical expression by moving any constants or terms without radicals to the opposite side of the equation.

Step 2: Square both sides of the equation to eliminate the radical.

Step 3: Solve the resulting equation for the variable.

Step 4: Check the solutions obtained by substituting them back into the original equation. This is important as sometimes extraneous solutions may arise. An extraneous solution is a solution that does not satisfy the original equation.

Let's work through an example to illustrate the process:

Example: Solve the equation √(2x + 5) = 7.

Step 1: Isolate the radical expression by subtracting 5 from both sides of the equation to obtain √(2x) = 2.

Step 2: Square both sides of the equation to eliminate the radical, resulting in 2x = 4.

Step 3: Solve for x by dividing both sides of the equation by 2, giving x = 2.

Step 4: Check the solution by substituting x = 2 back into the original equation. √(2(2) + 5) = 7. Simplifying, we get √9 = 7, which is true.

Therefore, the solution to the equation √(2x + 5) = 7 is x = 2.

Keep practicing and mastering the skills of solving radical equations! You're on your way to becoming a math superstar!