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 of the values of x.

Example 3:

Since the index of the radical is odd, there is no restriction on the values

of *x*.

- Add 8 to both sides of the equation so that the radical term
is isolated.

- Raise both sides of the equation to the third power.
*x*-7=125 - Add 7 to both sides of the equation
*x*=132

The answer is *x*=132.

Check the solution by substituting 132 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 5.

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

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

If you would like to go back to the equation table of contents, click on contents.

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