

Solving Radical Equations in One Variable Algebraically
• Solve squareroot 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 a^{n} = b^{n}
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
than one radical, choose one of the radicals
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
solve radial equations, therefore
apparent solutions must be checked . The
solution must be in the domain of the
radial expression. 
Solving Radial Equations

Solution

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Solution

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Solution

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Example 

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

Example 

Solve
Solution

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