 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.

Example 2: First make note of the fact that you cannot take the square root of a negative number. Therefore, • Isolate the term and simplify.  • Square both sides of the equation. 5x+3=9

• Isolate the x.

5x=6 The answer is 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: 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

(and hence the solution) on the graph is If you would like to work another problem, click

If you would like to test yourself by working some problems similar to

this example, clicks here.

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