Solving Radical Equations

Solving Radical Equations

By Jordan Feierabend

​Solving Equations

Equations with radicals that have variables in their radicands are called radical equations. An example of a radical equation is 2 √—x + 1 = 4.

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​Solving Equations

To solve a radical equation, follow these steps:

Step 1 Isolate the radical on one side of the equation, if necessary.

Step 2 Raise each side of the equation to the same exponent to eliminate the

radical and obtain a linear, quadratic, or other polynomial equation.

Step 3 Solve the resulting equation using techniques you learned in previous chapters. Check your solution.

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Multiple Choice

Example 1 a

Solve (a) 2 √—x + 1 = 4

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Multiple Choice

Example 1 b

Solve (b) √— 2x − 9 − 1 = 2.

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Monitoring Progress 1

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Monitoring Progress 2

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Monitoring Progress 3

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Solving an Equation with an Extraneous Solution

Raising each side of an equation to the same exponent may introduce extraneous solutions. When you use this procedure, you should always check each apparent solution in the original equation.

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Multiple Choice

Example 3

Solve x + 1 = √—7x + 15 .

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Multiple Choice

Example 4

Solve √—x + 2 + 1 = √—3 − x .

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Monitoring Progress 5

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Monitoring Progress 6

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Monitoring Progress 7

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Solving an Equation with a Rational Exponent

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Poll

Example 5

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MP 8

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