Algebra Tutorials! Home Exponents and Radicals Division of Radicals Exponents and Radicals RADICALS & RATIONAL EXPONENTS Radicals and Rational Exponents Radical Equations Solving Radical Equations Roots and Radicals RADICAL EQUATION 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 exponential_and_radical_properties Roots, Radicals, and Root Functions Multiplication of Radicals Solving Radical Equations Radical Expressions and Equations SOLVING RADICAL 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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 Number of inequalities to solve: 23456789
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# Solving Radical Equations in One Variable Algebraically

• Solve square-root equations in one variable algebraically
• Solve radical equations in one variable algebraically
• Solve equations containing variable expressions with
rational exponents algebraically
Principle of Powers

If a=b ,then an = bn

If you begin with an equation that is true
and you raise both sides of the equation
to the same power ,the fault is a true
equation.

Steps to Solve a Radical Equation

1. Isolate the radical. If the equation has more
to isolate.

2. Raise each side of the equation to a power
equal to the index of the radical.

3. Solve the resulting equation. If the equation
still has a radical, repeats steps 1 and 2.

4. Check the potential solutions in the original
equation.

Solve Algebraically Check! No solution Extraneous Solutions

Extraneous solutions can occur when we
apparent solutions must be checked .

The solution must be in the domain of the Solution Check Solution Checks Solution Check Solution Checks Solution Check Solution Checks

 Example Solve Solution The ± is needed because your are taking the square root Solutions Checks

 Example Solve Solution  Solution Checks