Vocabulary Refresher
The radicand refers to the number under the radical sign. In the radical below, the radicand is the number '5'.
![Picture of radicand](images/simplify-radicals/picture-of-radicand.png)
Examples
Example 1 of Multiplying Square roots
![Example 1 of mulitplying square roots](images/multiply-radicals/root5-by-roo15.gif)
Check to see if you can simplify either of the square roots (
). If you can, then simplify!
Both square roots are already simplified so skip this step.
Multiply the radicands together.
![Example 1.2](images/multiply-radicals/example1-step2.gif)
Example 2. A slightly more complex example
![Example 2 of mulitplying square roots](images/multiply-radicals/example-2/example-2.gif)
Check to see if you can simplify either of the square roots(
). If you can, then simplify!
can indeed be simplified:
Multiply the radicands together.
![Example 2.2](images/multiply-radicals/example-2/example-2-multiply-step.gif)
Practice Problems
Multiply the square roots below and express each answer in simplest radical form.
Problem 1
This problem is similar to example 1 because you can not simplify either of the square roots.
Step 1Multiply.
![Problem 1.2](images/multiply-radicals/problem2/problem2-step1.gif)
Problem 2
Problem 3
Problem 4
This problem is similar to example 2 because the square roots can be simplified. The only difference is that both square roots, in this problem, can be simplified.
Step 1![Problem 4.1](images/multiply-radicals/problem5/problem5-simplifiy.gif)
Multiply.
![Problem 4.2](images/multiply-radicals/problem5/problem5-multiply.gif)
Problem 5
This problem is similar to example 2 because the square roots can be simplified. The only difference is that both square roots, in this problem, can be simplified.
Step 1![Root 18 simplified](images/multiply-radicals/example-2/root-18-simplified.gif)
![Problem 5.1](images/multiply-radicals/problem4/problem4-step1.gif)
Multiply.
![Problem 5.2](images/multiply-radicals/problem3/problem2-step2.gif)
Problem 6
Problem 7
You may notice that this is the same as the problem prior problem (#6)...except that we have now added some coefficients.
Step 1![Problem 7.1](images/multiply-radicals/problem7/problem7-step2.gif)
Multiply.
![Problem 7.2](images/multiply-radicals/problem7/problem7-step3.gif)