Simplify Square Root of 39446

Here we will show you two methods that you can use to simplify the square root of 39446. In other words, we will show you how to find the square root of 39446 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.

√39446 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 39446 to simplify the square root of 39446. 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 39446. The factors of 39446 are 1, 2, 11, 22, 121, 163, 242, 326, 1793, 3586, 19723, and 39446. Furthermore, the greatest perfect square on this list is 121 and the square root of 121 is 11. Therefore, A equals 11.

B = Calculate 39446 divided by the greatest perfect square from the list of all factors of 39446. We determined above that the greatest perfect square from the list of all factors of 39446 is 121. Furthermore, 39446 divided by 121 is 326, therefore B equals 326.

Now we have A and B and can get our answer to 39446 in its simplest radical form as follows:

√39446 = A√B

√39446 = 11√326

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 39446 to simplify the square root of 39446 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 39446 and then take the square root of that product. The prime factors that multiply together to make 39446 are 2 x 11 x 11 x 163. When we strip out the pairs only, we get 11 x 11 = 121 and the square root of 121 is 11. Therefore, A equals 11.

B = Divide 39446 by the number (A) squared. 11 squared is 121 and 39446 divided by 121 is 326. Therefore, B equals 326.

Once again we have A and B and can get our answer to 39446 in its simplest radical form as follows:

√39446 = A√B

√39446 = 11√326

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

Simplify Square Root of 39447
Here is the next square root on our list that we have simplifed for you.