# 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:

Explanation:

Explanation:

### Example Question #3 : Multiplying And Dividing Radicals

Explanation:

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

### Example Question #4 : Multiplying And Dividing Radicals

Simplify.

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.

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.

Explanation:

and

Plug in the simplifed radicals into the equation:

### Example Question #7 : Multiplying And Dividing Radicals

Simplify and rationalize the denominator if needed,

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 #8 : Multiplying And Dividing Radicals

Simplify

Explanation:

To simplify, you must use the Law of Exponents.

First you must multiply the coefficients then add the exponents:

### Example Question #9 : Multiplying And Dividing Radicals

What is the product of  and ?

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 #10 : Multiplying And Dividing Radicals

Simplify

Explanation:

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