Exercise 7 Page 264

Solving a radical equation usually involves three main steps.

1. Isolate the radical on one side of the equation.
2. Raise each side of the equation to a power equal to the index of the radical to eliminate the radical.
3. Solve the resulting equation. Remember to check your results!

Now we can analyze the given radical equation. sqrt(x+6)-2=sqrt(x-2)Notice that in this equation there is an isolated radical with index equal to 2 on the right-hand side. Then, we will raise each side of the equation to the power of 2.

We obtained another radical equation. Let's now isolate the radical, sqrt(x+6), on one side of the equation.

Now, just like before, we will raise each side of the equation to the power of 2.

Next, we will check the solution by substituting 3 for x into the original equation. If the substitution produces a true statement, we know that our answer is correct. If it does not, then it is an extraneous solution.

Because our substitution produced a true statement, we know that our answer, x=3, is correct.