Algebra II : Solving Radical Equations

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #61 : Solving And Graphing Radicals

Solve:  

Possible Answers:

Correct answer:

Explanation:

Square both sides.

We will need to simplify the left side using the FOIL method.

A radical multiplied by itself becomes what's inside the radical.

The expression becomes:

Combine like-terms and rewrite the equation.

Isolate the radical by adding  and subtract 17 on both sides.  Then divide by two on both sides.

The radicals can be combined as one whole using the FOIL method.

Square both sides.

The  terms will cancel by subtracting the term on both side, and we can solve for .

Add  on both sides.

Multiply by four on both sides to eliminate the fraction.

Solve for x.

The answer is:  

Example Question #62 : Solving And Graphing Radicals

Solve:  

Possible Answers:

Correct answer:

Explanation:

Divide by four on both sides.

The equation becomes:  

Square both sides.

Add three on both sides.

Divide by three on both sides.

The answer is:  

Example Question #63 : Solving And Graphing Radicals

Solve:  

Possible Answers:

Correct answer:

Explanation:

Multiply by  on both sides.

Simplify both sides.

Square both sides to eliminate the radical.

Simplify both sides.

Divide by  on both sides.

The answer is:  

Example Question #64 : Solving And Graphing Radicals

Solve the radical:  

Possible Answers:

Correct answer:

Explanation:

Divide by two on both sides.  This is similar to multiplying by one-half.

Simplify both sides.

Cube both sides to eliminate the radical.

Divide by three on both sides.  This is similar to multiplying by one-third on both sides.

The answer is:  

Example Question #65 : Solving And Graphing Radicals

Solve the equation:  

Possible Answers:

Correct answer:

Explanation:

Subtract 31 from both sides of the equation.

Square both sides.

Simplify both sides.

Add nine on both sides.

The answer is:  

Example Question #66 : Solving And Graphing Radicals

Solve the equation:  

Possible Answers:

Correct answer:

Explanation:

To eliminate the radical, we will have to cube both sides.

The equation becomes:

Add seven on both sides.

Divide by three on both sides.

The answer is:  

Example Question #67 : Solving And Graphing Radicals

Solve:  

Possible Answers:

Correct answer:

Explanation:

Divide by three on both sides.

Rewrite the equation.

Raise both sides to the fourth power.

Simplify both sides.

Multiply by 81 on both sides to eliminate the fraction.

Subtract 729 from both sides.

Divide by negative 162 on both sides.

Reduce the fractions.  Double negatives will negate, turning the answer positive.

The answer is:  

Example Question #68 : Solving And Graphing Radicals

Evaluate:  

Possible Answers:

Correct answer:

Explanation:

Isolate the radical.  Add four on both sides.

Divide by three on both sides.  The equation becomes:

Raise both sides by four.

Subtract four on both sides.

Divide by negative two on both sides.

The answer is:  

Example Question #69 : Solving And Graphing Radicals

Solve the equation:  

Possible Answers:

Correct answer:

Explanation:

Multiply by six on both sides of the equation.

The equation becomes:

Cube both sides to eliminate the radical.

Add two on both sides.

Divide by five on both sides.

The answer is:  

Example Question #70 : Solving And Graphing Radicals

Solve the radical equation:  

Possible Answers:

Correct answer:

Explanation:

Add seven on both sides.

Square both sides.  This will eliminate the radical.

Add five on both sides.

Divide both sides by negative 6 and reduce the fraction.

The answer is:  

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