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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.

Work the following problems. Click on Solution, if you want to review the solutions.

Problem 2.7a: $\sqrt[7]{5x+3}+\displaystyle \frac{2}{3}=\displaystyle \frac{8}{3}$
Solution

Problem 2.7b: $\sqrt[4]{10x-19}+3=6$
Solution

Problem 2.7c: $\sqrt[3]{\displaystyle \frac{13x+5}{5}}+10=13$
Solution

Problem 2.7d: $\sqrt[11]{\displaystyle \frac{3x+11}{2}}+5=4$
Solution

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

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Author:Nancy Marcus