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*.Problem 2.2b:

Answer: 32.666667.

Solution:

- Add 9 to both sides of the equation so that the radical term is isolated.
- Square both sides of the equation.
3

*x*+2=100 - Subtract 2 from both sides of the equation.
3

*x*=98 - The answer is 32.666667.
- Check the solution by substituting