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 4:

Since the index of the radical is odd, there is no restrictions on the value of x in this problem.

Raise both sides of the equation to the power 3.

Subtract 15 from both sides of the equation

Multiply both sides of the equation by

The answer is x = -10.5

Check the solution by substituting -10.5 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.

[Algebra] [Trigonometry]
[Geometry] [Differential Equations]
[Calculus] [Complex Variables] [Matrix Algebra]

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Author:Nancy Marcus