All Algebra II Resources
Example Question #1 : Multiplying And Dividing Radicals
Multiply and express the answer in the simplest form:
Example Question #2 : Multiplying And Dividing Radicals
Example Question #3 : Multiplying And Dividing Radicals
FOIL with difference of squares. The multiplying cancels the square roots on both terms.
Example Question #4 : Multiplying And Dividing Radicals
We can solve this by simplifying the radicals first:
Plugging this into the equation gives us:
Example Question #5 : Multiplying And Dividing Radicals
Note: the product of the radicals is the same as the radical of the product:
Once we understand this, we can plug it into the equation:
Example Question #6 : Multiplying And Dividing Radicals
We can simplify the radicals:
Plug in the simplifed radicals into the equation:
Example Question #7 : Multiplying And Dividing Radicals
Simplify and rationalize the denominator if needed,
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
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 ?
First, simplify to .
Then set up the multiplication problem:
Multiply the terms outside of the radical, then the terms under the radical:
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
To divide the radicals, simply divide the numbers under the radical and leave them under the radical:
Then simplify this radical: