High School Math : Radicals

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #16 : Factoring Radicals

Simplify the following radical expression:

Possible Answers:

Correct answer:

Explanation:

Simplify the radical expression:

Example Question #1 : Simplifying Radicals

Simplify the expression:

Possible Answers:

.

Correct answer:

Explanation:

Use the multiplication property of radicals to split the fourth roots as follows:

Simplify the new roots:

Example Question #2 : Adding And Subtracting Radicals

Find the value of .

Possible Answers:

Correct answer:

Explanation:

To solve this equation, we have to factor our radicals.  We do this by finding numbers that multiply to give us the number within the radical. 

Add them together:

4 is a perfect square, so we can find the root:

Since both have the same radical, we can combine them:

Example Question #81 : Algebra Ii

Factor and simplify the following radical expression:

Possible Answers:

Correct answer:

Explanation:

Begin by using the FOIL method (First Outer Inner Last) to expand the expression.

Now, combine like terms:

Example Question #1 : Using Radicals With Elementary Operations

What is the value of ?

Possible Answers:

Correct answer:

Explanation:

When combining terms involving radicals, we can only combine the ones that have the same radical.  For this problem, that means  has to stay on its own while we can combine  and  into .  The simple integers can be combined too, giving us our answer with three seperate terms.

Example Question #2 : Using Radicals With Elementary Operations

Simplify the expression:.

Possible Answers:

Correct answer:

Explanation:

Exponents in the denominator can be subtracted from exponents in the numerator.

Recall that .

Therefore, .

 

Example Question #3 : Using Radicals With Elementary Operations

Simplify:

Possible Answers:

Correct answer:

Explanation:

Try to group factors in pairs to get perfect squares under the square root:

Example Question #82 : Algebra Ii

Solve for :

Possible Answers:

Correct answer:

Explanation:

To solve for  in the equation 

Square both sides of the equation 

Set the equation equal to  by subtracting the constant  from both sides of the equation.

Factor to find the zeros:

This gives the solutions 

.

Verify that these work in the original equation by substituting them in for . This is especially important to do in equations involving radicals to ensure no imaginary numbers (square roots of negative numbers) are created.

Example Question #83 : Algebra Ii

Solve the following radical expression:

Possible Answers:

Correct answer:

Explanation:

Begin by subtracting  from each side of the equation:

 

Now, square the equation:

 

Solve the linear equation:

Example Question #84 : Algebra Ii

Solve the following radical expression:

Possible Answers:

Correct answer:

Explanation:

Begin by squaring both sides of the equation:

 

Combine like terms:

 

Once again, square both sides of the equation:

 

Solve the linear equation:

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