• solve simple radical equations in one variable.

• give examples of simple radical equations showing how extraneous solutions may arise.

​Learning Targets

What is Radical Expression

A radical expression is an equation that has a variable in a radicand or has a variable with a radical expression

Applications of Radical Equations

Steps to solve a radical equation:

STEP 1: Isolate the radical on one side of the equation (if possible)

STEP 2: Raise each side of the equation to a power equal to the index of the radical to eliminate the radical

STEP 3: Solve the remaining polynomial equation. CHECK YOUR RESULTS.

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.

​Extraneous Solutions

​Note:

When we use a radical sign, it indicates the principal or positive root. If an equation has a radical with an even index equal to a negative number, that equation will have no solution.

If one side of an equation with a square root is a binomial, we use the Product of Binomial Squares Pattern when we square it. Don’t forget the middle term!

​Binomial Squares

​Rational Exponents