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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 ( Root 5 and 15 ). If you can, then simplify!

Both square roots are already simplified so skip this step.

Step 2

Multiply the radicands together.

Example 1.2
Step 3
Simplify
Example 1.3
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( Example 2.1 ). If you can, then simplify!

Root 18 can indeed be simplified: Root 18 simplified

Step 2

Multiply the radicands together.

Example 2.2
Step 3
Simplify
Example 2.3

Practice Problems

Multiply the square roots below and express each answer in simplest radical form.

Problem 1
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.

Problem 1.2
Step 3
Simplify
Problem 1.3
Problem 2
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!
Root 8 can be simplified: Root 8 simplified
Step 2
Multiply
Problem 2.2
Step 3
Simplify
Problem 2.3 is already in simplest form so you are done.
Problem 3
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!
Root 18 can indeed be simplified: Root 18 simplified
Step 2
Multiply
Problem 3.2
Step 3
Simplify
Problem 3.3
Problem 4
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!
Problem 4.1
Step 2

Multiply.

Problem 4.2
Step 3
Simplify
This radical expression is already simplified so you are done.
Problem 5
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!
Root 18 simplified Problem 5.1
Step 2

Multiply.

Problem 5.2
Step 3
Simplify
This radical expression is already simplified so you are done.
Problem 6
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!
Problem 6.1
Step 2

Multiply.

Problem 6.2
Step 3
Simplify
Problem 6.3
Problem 7
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!
Problem 7.1
Step 2

Multiply.

Problem 7.2
Step 3
Simplify
Problem 7.3
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