How to Solve a Radical Equation

1
How to Solve a Radical Equation

• Consider the Problem.
• Put the radicals on different sides of the equals
  sign.
• Square both sides.
• Move all the terms that dont involve radicals to
  one side.
• Square both sides again. (If radicals remain).
• Finish Solving
• Check your solutions in the original equation.
• State your conclusion

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2
Warning
To succeed at solving these problems, you must be
able to solve problems on your own. This
means a.) No notes. b.) No calculator. c.) No
tutor or friend. To accomplish this, you must be
able to perform each step prior to seeing it
carried out. So, after you think you understand
the process, try another problem. Rather than
looking at this example to direct you, look at it
to check your progress and understanding. Good
luck and enjoy some fun problems
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Step 1
Consider the Problem.
Notice that there are two radicals in this
equation
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Step 2
Put the radicals on different sides of the equals
sign.
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Step 3
Square both sides.
Write out all squares involving addition as a
product.
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Step 4
Move all the terms that dont involve radicals to
one side.
Note If your original problem only contains one
radical, this is your first step.
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Step 5
Square both sides again. (If radicals remain).
Write out all squares involving addition as a
product.
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Step 6
Finish Solving
a.) Move all terms to one side.
b.) Solve as you see fit in this case by
factoring.
x 7 or x ? 1
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Step 7
Check your solutions in the original equation.
True
False
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Step 8
State your conclusion
Note Do not forget to check your solutions.
Radical equations can have extraneous solutions.
It is even possible for them to have no solution.
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