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

Problem2.6d:

Answer: 1,364

Solution:

Rewrite the radical terms as exponential terms.

Raise both sides of the equation to the power 12 and simplify.

The answer is 1,364.

Check the solution by substituting 1,364 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: 2

Since the left side of the original equation equals the right side of the original equation after we substituted 1,364 for x, then x=1,364 is a solution.

You can also check the answer by graphing the equation:

The graph represents the right side of the original equation minus the left side of the original equation. Since there is one x-intercept at 1,364, the solution is 1,364.

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