Simplify Square Root of 13851

Here we will show you two methods that you can use to simplify the square root of 13851. In other words, we will show you how to find the square root of 13851 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.

√13851 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 13851 to simplify the square root of 13851. 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 13851. The factors of 13851 are 1, 3, 9, 19, 27, 57, 81, 171, 243, 513, 729, 1539, 4617, and 13851. Furthermore, the greatest perfect square on this list is 729 and the square root of 729 is 27. Therefore, A equals 27.

B = Calculate 13851 divided by the greatest perfect square from the list of all factors of 13851. We determined above that the greatest perfect square from the list of all factors of 13851 is 729. Furthermore, 13851 divided by 729 is 19, therefore B equals 19.

Now we have A and B and can get our answer to 13851 in its simplest radical form as follows:

√13851 = A√B

√13851 = 27√19

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 13851 to simplify the square root of 13851 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 13851 and then take the square root of that product. The prime factors that multiply together to make 13851 are 3 x 3 x 3 x 3 x 3 x 3 x 19. When we strip out the pairs only, we get 3 x 3 x 3 x 3 x 3 x 3 = 729 and the square root of 729 is 27. Therefore, A equals 27.

B = Divide 13851 by the number (A) squared. 27 squared is 729 and 13851 divided by 729 is 19. Therefore, B equals 19.

Once again we have A and B and can get our answer to 13851 in its simplest radical form as follows:

√13851 = A√B

√13851 = 27√19

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

Simplify Square Root of 13852
Here is the next square root on our list that we have simplifed for you.