Radical or irrational equations
Solving irrational or radical equations
Radical or irrational equations
Any equation where the variable is inside a radical is called an irrational equation.
To solve an irrational equation we should isolate one of the radicals on one side of the equation and get other radicals and terms on the other side of the equation.
Rise both sides of the equation to a power to remove the radical, and then simplify and solve as we do with any equations. Repeat the procedure until all radicals are removed.
Substitute answers back into original equation to make sure that solutions are valid, as there could be some additional or extraneous solutions that do not satisfy the original equation.
That is, raising equation to a power can lead to extraneous solutions. We must check to be certain which of obtained values are true solutions.
Solving irrational or radical equations
 Example:  Solve the irrational equation
Solution:  First isolate the radical and then square both sides of the equation,
Checking for the solutions:
Solution:
 Example:  Solve the irrational equation
 Solution:
Checking for the solutions:
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