Simplify Square Root of 39412

Here we will show you two methods that you can use to simplify the square root of 39412. In other words, we will show you how to find the square root of 39412 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.

√39412 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 39412 to simplify the square root of 39412. 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 39412. The factors of 39412 are 1, 2, 4, 59, 118, 167, 236, 334, 668, 9853, 19706, and 39412. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 39412 divided by the greatest perfect square from the list of all factors of 39412. We determined above that the greatest perfect square from the list of all factors of 39412 is 4. Furthermore, 39412 divided by 4 is 9853, therefore B equals 9853.

Now we have A and B and can get our answer to 39412 in its simplest radical form as follows:

√39412 = A√B

√39412 = 2√9853

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 39412 to simplify the square root of 39412 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 39412 and then take the square root of that product. The prime factors that multiply together to make 39412 are 2 x 2 x 59 x 167. 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 39412 by the number (A) squared. 2 squared is 4 and 39412 divided by 4 is 9853. Therefore, B equals 9853.

Once again we have A and B and can get our answer to 39412 in its simplest radical form as follows:

√39412 = A√B

√39412 = 2√9853

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

Simplify Square Root of 39413
Here is the next square root on our list that we have simplifed for you.