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 Depdendent Variable

 Number of equations to solve: 23456789
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 Dependent Variable

 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