Solving Radical Equations

Solving Radical Equations

Let's look at ways we can solve radical equations

• 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.

Open Ended

Solve $$\sqrt[]{3m+2}-5\ =\ 0$$

Open Ended

Solve $$\sqrt[]{10z+1}-2\ =\ 0$$

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.

Open Ended

Solve $$\sqrt[]{2r-3}+5\ =\ 0$$

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

Open Ended

Solve $$\sqrt[]{x-2}+2\ =\ x$$

​Rational Exponents

Fill in the Blanks

Solve $\left(9x+9\right)^{\frac{1}{4}}-2=1$