# Algebra II : Multiplying and Dividing Radicals

## Example Questions

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### 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:

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

### Example Question #3 : 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 #4 : 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 #5 : 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 #6 : 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 #7 : 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 #8 : 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 #9 : 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: .

### Example Question #10 : Multiplying And Dividing Radicals

Solve and simplify. Possible Answers:     Correct answer: Explanation:

When multiplying radicals, just take the values inside the radicand and perfom the operation.  can't be reduced so this is the final answer.

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