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 1:

First make a note of the fact that you cannot take the square root of a negative number. Therefore, or .

Square both sides of the equation.

Add 8 to both sides of the equation.

Check the solution by substituting 17 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.

If you would like to work another example, click on example.

If you would like to test yourself by working some problems similar to this example, click on problem.