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 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 answer.
• If the index of the radical is even, many times there will be a restriction on the values of x.

Example 1:

First make a note of the fact that you cannot take the square root of a negative number. Therefore, Add 4 to both sides of the equation so that the radical term is isolated.

Square both sides of the equation.

x - 10 = 16

Add 10 to both sides of the equation

x = 26

The answer is x = 26.

Check the solution by substituting 26 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: 0.

You can also check the answer by graphing the left side of the equation:

Since the right side of the equation is 0, the right side of the equation represents the x-axis. The solution will be the x-intercept. The x-intercept (and hence the solution) on the graph is 26.

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.

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