Algebra II : Radicals

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #11 : Solving Radical Equations

Solve for .

Possible Answers:

Correct answer:

Explanation:

 Subtract  on both sides.

 Square both sides to get rid of the radical.

 Divide  on both sides.

Example Question #12 : Solving And Graphing Radicals

Solve for .

Possible Answers:

Correct answer:

Explanation:

 Subtract  on both sides. Since  is greater than  and is negative, our answer is negative. We treat as a normal subtraction.

 Square both sides to get rid of the radical. When squaring negative values, they become positive.

 Subtract  on both sides. 

Example Question #11 : Solving Radical Equations

Solve for .

Possible Answers:

Correct answer:

Explanation:

  Square both sides to get rid of the radical. 

 Subtract  on both sides. 

 Add  on both sides.

 Divide  on both sides.

Example Question #12 : Solving Radical Equations

Solve for .

Possible Answers:

Correct answer:

Explanation:

 Divide  on both sides.

 Square both sides to get rid of the radical. 

 Subtract  on both sides. Since  is greater than  and is negative, our answer is negative. We treat as a normal subtraction.

Example Question #13 : Solving Radical Equations

Solve for .

Possible Answers:

Correct answer:

Explanation:

 Square both sides to get rid of the radical.

 This is a set-up of a quadratic equation Subtract  on both sides.

  We need to find two terms that are factors of the c term that add up to the b term. 

 

 Subtract  on both sides. Since  is greater than  and is negative, our answer is negative. We treat as a normal subtraction.

Example Question #1571 : Mathematical Relationships And Basic Graphs

Solve:

Possible Answers:

Correct answer:

Explanation:

To solve this problem, first square both sides: . Then, solve for x, which is 40.

Example Question #4232 : Algebra Ii

Solve and simplify:

Possible Answers:

Correct answer:

Explanation:

To solve for x, first we must isolate the radical on one side:

Next, square both sides to eliminate the radical:

Now, take the cube root of each side to find x:

Finally, factor the term inside the cube root and see if any cubes can be pulled out of the radical:

Example Question #21 : Solving Radical Equations

Solve:  

Possible Answers:

Correct answer:

Explanation:

Subtract 14 on both sides.

Simplify both sides.

To eliminate the radical, square both sides.

Simplify both sides.

Divide by two on both sides.

The answer is:  

Example Question #23 : Solving And Graphing Radicals

Solve the equation:  

Possible Answers:

Correct answer:

Explanation:

Subtract  from both sides to group the radicals.

Square both sides.

Use the FOIL method to simplify the right side.

Combine like-terms.

Subtract one from both sides, and add  on both sides.

The equation becomes:  

Divide by two on both sides and distribute the terms inside the radical.

Square both sides.

Simplify the right side by FOIL method.

Subtract  on both sides.  This is the same as subtracting  on both sides.

Subtract  on both sides.  The equation will become:

Multiply by four on both sides to eliminate the fractional denominator.

Use the quadratic equation to solve for the roots.

Simplify the radical and fraction.

Substitute the values of  and  back into the original equation, and only  will satisfy both sides of the equation.

The answer is:  

Example Question #24 : Solving And Graphing Radicals

Solve, and ensure there are no radicals in the denominator

Possible Answers:

None of these

Correct answer:

Explanation:

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