

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: 


Example:
Solve the
irrational equation 



Checking
for the solutions: 









College
algebra contents D 



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