EQUATIONS CONTAINING VARIABLES UNDER ONE OR MORE RADICALS

Note::

• In order to solve for x, you must isolate x.

• In order to isolate x, you must remove it from under the radical.

• If there is just one radical in the equation, isolate the radical.

• Then raise both sides of the equation to a power equal to the index of the radical.

• With these types of equations, sometimes there are extraneous solutions; therefore, you must check your answers.

• If the index of the radical is even, many times there will be a restriction on the values of x.

  Problem 2.2a:

  Answer:

  Solution:

  Since the index of the radical is even, the quantity under the

  radical cannot be negative and

  

• Square both sides of the original equation.

  

  5x-11=36

• Add 11 to both sides

  5x=47

  

Check the solution by substituting in the original equation

for x. If the left side of the equation equals the right side of the equation

after the substitution, you have found the correct answer.

Left side:

Right side: Since the left side of the original equation equals the right side of the

original equation when you substitute , the answer is correct.

You can also check the answer by graphing

(the left side of the original equation minus the right side of the

original equation). The solution will be the x-intercept. The x-intercept

is

If you would like to review the solution to problem 2.2b,click on problem

Links to S221102

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