EQUATIONS CONTAINING VARIABLES UNDER ONE OR MORE RADICALS
- In order to solve for x, you must isolate x.
- In order to isolate x, you must remove it from under the radial.
- 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.
Note: Since the index is even, the expression under the radical sign
cannot be negative, .
Isolate the radical term.
Raise both sides of the equation to the power 6.
Isolate the x:
The answer is x=58,821
Check the solution by substituting 58,821 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.
Since the left side of the original equation equals the right side of the
original equation after you substitute 58,821 for x, then 58,821 is a
- Left side:
- Right Side: 2
You can also check your solution by graphing the function
The above function is formed by subtracting the right side of the original
equation from the left side of the original equation. The x-intercept of the
graph is the solution to the original equation. As you can see, the
x-intercept is 58,821, verifying our solution.
If you would like to test yourself by working some
problems similar to this example, click on Problem.
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