Simplify Square Root of 3627

Here we will show you two methods that you can use to simplify the square root of 3627. In other words, we will show you how to find the square root of 3627 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.

√3627 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 3627 to simplify the square root of 3627. 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 3627. The factors of 3627 are 1, 3, 9, 13, 31, 39, 93, 117, 279, 403, 1209, and 3627. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 3627 divided by the greatest perfect square from the list of all factors of 3627. We determined above that the greatest perfect square from the list of all factors of 3627 is 9. Furthermore, 3627 divided by 9 is 403, therefore B equals 403.

Now we have A and B and can get our answer to 3627 in its simplest radical form as follows:

√3627 = A√B

√3627 = 3√403

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 3627 to simplify the square root of 3627 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 3627 and then take the square root of that product. The prime factors that multiply together to make 3627 are 3 x 3 x 13 x 31. When we strip out the pairs only, we get 3 x 3 = 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Divide 3627 by the number (A) squared. 3 squared is 9 and 3627 divided by 9 is 403. Therefore, B equals 403.

Once again we have A and B and can get our answer to 3627 in its simplest radical form as follows:

√3627 = A√B

√3627 = 3√403

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

Simplify Square Root of 3628
Here is the next square root on our list that we have simplifed for you.