How to Multiply Square Roots

Examples, formula and the Steps!

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

Video on How To Multiply Square Roots

Examples

Example 1 of Multiplying Square roots
Example 1 of mulitplying square roots Step 1

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

Step 2

Multiply the radicands together

exmaple 1 step 2

Step 3
Example 2. A slightly more complex example
Example 2 of mulitplying square roots Step 1

Check to see if you can simplify either of the square roots(. )If you can, then simplify!

can indeed be simplified :

Step 2

Multiply the radicands together

 step 2

Step 3

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 1
Check to see if you can simplify either of the square roots. If you can, then simplify!
Skip this since both square roots are already simplified.
Step 2

Multiply

 step 2
Step 3
Problem 2

This problem is similar to example 2 because 1 of the square roots can be simplified

Step 1
Check to see if you can simplify either of the square roots. If you can, then simplify!
can be simplified:
Step 2
Multiply
 step 2
Step 3
is already in simplest form so you are done.
Problem 3
This problem is similar to example 2 because 1 of the square roots can be simplified Step 1
Check to see if you can simplify either of the square roots. If you can, then simplify!
can indeed be simplified:
Step 2
Multiply
 step 2
Step 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
Check to see if you can simplify either of the square roots. If you can, then simplify!
Step 2

Multiply

 step 2
Step 3
This radical expression is already simplified so you are done
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
Check to see if you can simplify either of the square roots. If you can, then simplify!

Step 2

Multiply

 step 2
Step 3
This radical expression is already simplified so you are done
Problem 6

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
Check to see if you can simplify either of the square roots. If you can, then simplify!
Step 2

Multiply

 step 2
Step 3
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
Check to see if you can simplify either of the square roots. If you can, then simplify!
Step 2

Multiply

 step 2
Step 3