Algebra II : Multiplying and Dividing Radicals

Study concepts, example questions & explanations for Algebra II

varsity tutors app store varsity tutors android store

Example Questions

← Previous 1 3 4 5 6 7

Example Question #1 : Multiplying And Dividing Radicals

Multiply and express the answer in the simplest form:

Possible Answers:

Correct answer:

Explanation:

Example Question #2 : Multiplying And Dividing Radicals

Possible Answers:

Correct answer:

Explanation:

Example Question #3 : Multiplying And Dividing Radicals

Possible Answers:

Correct answer:

Explanation:

FOIL with difference of squares.  The multiplying cancels the square roots on both terms.  

Example Question #4 : Multiplying And Dividing Radicals

Simplify. 

Possible Answers:

Correct answer:

Explanation:

We can solve this by simplifying the radicals first: 

Plugging this into the equation gives us: 

Example Question #5 : Multiplying And Dividing Radicals

Simplify.

Possible Answers:

Correct answer:

Explanation:

Note: the product of the radicals is the same as the radical of the product: 

  which is 

Once we understand this, we can plug it into the equation:

 

Example Question #6 : Multiplying And Dividing Radicals

Simplify.

Possible Answers:

Correct answer:

Explanation:

We can simplify the radicals:

     and    

Plug in the simplifed radicals into the equation:

Example Question #7 : Multiplying And Dividing Radicals

Simplify and rationalize the denominator if needed,

Possible Answers:

Correct answer:

Explanation:

We can only simplify the radical in the numerator:  

 

Plugging in the simplifed radical into the equation we get:

Note: We simplified further because both the numerator and denominator had a "4" which canceled out. 

Now we want to rationalize the denominator,

 

Example Question #4 : Multiplying And Dividing Radicals

Simplify

Possible Answers:

Correct answer:

Explanation:

To simplify, you must use the Law of Exponents.

First you must multiply the coefficients then add the exponents:

Example Question #5 : Multiplying And Dividing Radicals

What is the product of  and ?

Possible Answers:

Correct answer:

Explanation:

First, simplify  to .

Then set up the multiplication problem:

 .

Multiply the terms outside of the radical, then the terms under the radical:

  then simplfy:  

The radical is still not in its simplest form and must be reduced further: 

. This is the radical in its simplest form. 

Example Question #6 : Multiplying And Dividing Radicals

Simplify 

Possible Answers:

Correct answer:

Explanation:

To divide the radicals, simply divide the numbers under the radical and leave them under the radical: 

 

Then simplify this radical: 

.

← Previous 1 3 4 5 6 7
Learning Tools by Varsity Tutors

Incompatible Browser

Please upgrade or download one of the following browsers to use Instant Tutoring: