Simplify: ( y − 3 ) 2 . ( y − 3 ) 2 .
If you missed this problem, review Example 5.31.
Solve: 2 x − 5 = 0 . 2 x − 5 = 0 .
If you missed this problem, review Example 2.2.
Solve n 2 − 6 n + 8 = 0 . n 2 − 6 n + 8 = 0 .
If you missed this problem, review Example 6.45.
In this section we will solve equations that have a variable in the radicand of a radical expression. An equation of this type is called a radical equation .
An equation in which a variable is in the radicand of a radical expression is called a radical equation.
As usual, when solving these equations, what we do to one side of an equation we must do to the other side as well. Once we isolate the radical, our strategy will be to raise both sides of the equation to the power of the index. This will eliminate the radical.
Solving radical equations containing an even index by raising both sides to the power of the index may introduce an algebraic solution that would not be a solution to the original radical equation. Again, we call this an extraneous solution as we did when we solved rational equations.
In the next example, we will see how to solve a radical equation. Our strategy is based on raising a radical with index n to the n th power. This will eliminate the radical.