Algebra II : Solving Radical Equations

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #81 : Solving And Graphing Radicals

Solve the equation:  

Possible Answers:

Correct answer:

Explanation:

Raise both sides by the power of three in order to eliminate the radical.

Add nine on both sides.

Divide by negative six on both sides.

The answer is:  

Example Question #82 : Solving And Graphing Radicals

Solve:  

Possible Answers:

Correct answer:

Explanation:

Cube both sides to eliminate the radical.

The equation becomes:  

Multiply by eight on both sides to eliminate the fraction.

Add 48 on both sides.

Divide by 24 on both sides.

The answer is:  

Example Question #83 : Solving And Graphing Radicals

Solve:  

Possible Answers:

Correct answer:

Explanation:

Subtract two from both sides.

Square both sides in order to eliminate the radical.

Divide by nine on both sides.

The right side is irreducible.

The answer is:  

Example Question #84 : Solving And Graphing Radicals

Solve the radical:  

Possible Answers:

Correct answer:

Explanation:

Square both sides in order to eliminate the radical.

The equation becomes:

Subtract three from both sides.

Divide by negative five on both sides.

The answer is:  

Example Question #85 : Solving And Graphing Radicals

Solve:  

Possible Answers:

Correct answer:

Explanation:

Add three on both sides.

Raise both sides by the power of five to eliminate the radical.

Divide by negative three on both sides.

The answer is:  

Example Question #86 : Solving And Graphing Radicals

Solve the equation:  

Possible Answers:

Correct answer:

Explanation:

The radicals can be combined as one radical by multiplying the two inner terms together.

The equation becomes:

Add 10 on both sides.

Simplify both sides.

Square both sides.

Divide by ten on both sides.

The answer is:  

Example Question #87 : Solving And Graphing Radicals

Solve the radical:  

Possible Answers:

Correct answer:

Explanation:

Rewrite the radicals so that they are in exponential form.

The equation becomes:

Raise both sides by the power of four to eliminate the fractional exponents.

Divide by two on both sides.

The answer is:  

Example Question #88 : Solving And Graphing Radicals

Solve:  

Possible Answers:

Correct answer:

Explanation:

Evaluate by changing the base of the left term.

Now that both bases are common, set the powers equal and solve for x.

Add 8 on both sides.

Divide by ten on both sides.

The answer is:  

Example Question #89 : Solving And Graphing Radicals

Evaluate:  

Possible Answers:

Correct answer:

Explanation:

Cube both sides to eliminate the radical.

Add eight on both sides.

Divide by 2 on both sides.

The answer is:  

Example Question #90 : Solving And Graphing Radicals

Solve:  

Possible Answers:

Correct answer:

Explanation:

Solve by first dividing both sides by two.

Simplify both sides.

Cube both sides.

Subtract two from both sides.

Divide by negative five on both sides.

The answer is:  

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