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 Depdendent Variable

 Number of equations to solve: 23456789
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 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

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 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

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Now that we have learned how to work with radical expressions we will move on to
solving. We must use caution when solving radical equations because the following steps
may lead to extraneous solutions, solutions that do not solve the original equation.

 Solve Step 2: Raise both sides to the nth power. (In this case, square both sides) Step 1: Isolate the radical. Step 3: Solve like normal. Step 4: Check to see if your answers solve the original equation.

Whenever we raise both sides of an equation to an even power we introduce the
possibility of extraneous solutions so the check is essential here.

A. Solve

The root determines what power to raise both sides to. For example, if we have a cubed
root we must raise both sides to the 3rd power. The property that we are using is
for integers n > 1 and positive real numbers x. After eliminating the radical,
we will most likely be left with either a linear or quadratic equation to solve.

The check mark indicates that we have actually checked that the value is a solution to the
equation, do not dismiss this step, it is essential.

The next set of problems is actually my personal favorite because I grew up in Southern
California and I like to call them “totally” radical equations!

B. Solve

Students often have difficulty with radical expressions where we have more than one
radical expression. These require us to isolate each remaining radical expression and
raise both sides to the nth power until they are all eliminated. Be patient with these, go
slow and avoid short cuts.

Tip: Use the formulas to save a step when squaring binomials.

In the last problem, notice that I used the formula to square the following binomial.