High School Math : Radicals

Study concepts, example questions & explanations for High School Math

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Example Questions

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Example Question #85 : Algebra Ii

Solve the following radical expression:

Possible Answers:

No real solutions

Correct answer:

Explanation:

Begin by squaring both sides of the equation:

 

Now, combine like terms:

 

Factor the equation:

 

However, when plugging in the values,  does not work. Therefore, there is only one solution:

Example Question #86 : Algebra Ii

Solve the following radical expression:

Possible Answers:

Correct answer:

Explanation:

Begin by squaring both sides of the equation:

 

Now, combine like terms and simplify:

 

Once again, take the square of both sides of the equation:

 

Solve the linear equation:

Example Question #1 : Solving Radical Equations And Inequalities

Solve the following radical expression:

Possible Answers:

Correct answer:

Explanation:

Begin by taking the square of both sides:

 

Combine like terms:

 

Factor the equation and solve:

 

However, when plugging in the values,  does not work. Therefore, there is only one solution:

Example Question #2 : Solving Radical Equations And Inequalities

Solve the following radical expression:

Possible Answers:

Correct answer:

Explanation:

To solve the radical expression, begin by subtracting  from each side of the equation:

Now, square both sides of the equation:

Combine like terms:

Factor the expression and solve:

However, when plugged into the original equation,  does not work because the radical cannot be negative. Therefore, there is only one solution:

Example Question #3 : Solving Radical Equations And Inequalities

Solve the equation for .

 

 

 

 

 

 

 

Possible Answers:

Correct answer:

Explanation:

Add to both sides.

Square both sides.

Isolate .

Example Question #4 : Solving Radical Equations And Inequalities

Solve for :

Possible Answers:

Correct answer:

Explanation:

Begin by cubing both sides:

Now we can easily solve:

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