Simplify Square Root of 37684

Here we will show you two methods that you can use to simplify the square root of 37684. In other words, we will show you how to find the square root of 37684 in its simplest radical form using two different methods.

To be more specific, we have created an illustration below showing what we want to calculate. Our goal is to make "A" outside the radical (√) as large as possible, and "B" inside the radical (√) as small as possible.

√37684 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 37684 to simplify the square root of 37684. This is how to calculate A and B using this method:

A = Calculate the square root of the greatest perfect square from the list of all factors of 37684. The factors of 37684 are 1, 2, 4, 9421, 18842, and 37684. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 37684 divided by the greatest perfect square from the list of all factors of 37684. We determined above that the greatest perfect square from the list of all factors of 37684 is 4. Furthermore, 37684 divided by 4 is 9421, therefore B equals 9421.

Now we have A and B and can get our answer to 37684 in its simplest radical form as follows:

√37684 = A√B

√37684 = 2√9421

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 37684 to simplify the square root of 37684 to its simplest form possible. This is how to calculate A and B using this method:

A = Multiply all the double prime factors (pairs) of 37684 and then take the square root of that product. The prime factors that multiply together to make 37684 are 2 x 2 x 9421. When we strip out the pairs only, we get 2 x 2 = 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Divide 37684 by the number (A) squared. 2 squared is 4 and 37684 divided by 4 is 9421. Therefore, B equals 9421.

Once again we have A and B and can get our answer to 37684 in its simplest radical form as follows:

√37684 = A√B

√37684 = 2√9421

Simplify Square Root
Please enter another square root in the box below for us to simplify.

Simplify Square Root of 37685
Here is the next square root on our list that we have simplifed for you.