Exponents and Radicals
Division of Radicals
Exponents and Radicals
Radicals and Rational Exponents
Radical Equations
Solving Radical Equations
Roots and Radicals
Simplifying Radical Expressions
Radical Expressions
Solving Radical Equations
Solving Radical Equations
Exponents and Radicals
Exponents and Radicals
Roots;Rational Exponents;Radical Equations
Solving and graphing radical equations
Solving Radical Equations
Radicals and Rational Exponents
Roots, Radicals, and Root Functions
Multiplication of Radicals
Solving Radical Equations
Radical Expressions and Equations
Equations Containing Radicals and Complex Numbers
Square Roots and Radicals
Solving Radical Equations in One Variable Algebraically
Polynomials and Radicals
Roots,Radicals,and Fractional Exponents
Adding, Subtracting, and Multiplying Radical Expressions
Square Formula and Powers with Radicals
Simplifying Radicals
Exponents and Radicals Practice
Solving Radical Equations
Solving Radical Equations
Solving Radical Equations
Lecture-Radical Expressions
Radical Functions
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Solving Radical Equations

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.

Step 2: Raise both sides to
the nth power. (In this
case, square both sides)
Step 1: Isolate
the radical.

Step 3: Solve like
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.

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