Simplify Square Root of 25857

Here we will show you two methods that you can use to simplify the square root of 25857. In other words, we will show you how to find the square root of 25857 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.

√25857 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 25857 to simplify the square root of 25857. 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 25857. The factors of 25857 are 1, 3, 9, 13, 17, 39, 51, 117, 153, 169, 221, 507, 663, 1521, 1989, 2873, 8619, and 25857. Furthermore, the greatest perfect square on this list is 1521 and the square root of 1521 is 39. Therefore, A equals 39.

B = Calculate 25857 divided by the greatest perfect square from the list of all factors of 25857. We determined above that the greatest perfect square from the list of all factors of 25857 is 1521. Furthermore, 25857 divided by 1521 is 17, therefore B equals 17.

Now we have A and B and can get our answer to 25857 in its simplest radical form as follows:

√25857 = A√B

√25857 = 39√17

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 25857 to simplify the square root of 25857 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 25857 and then take the square root of that product. The prime factors that multiply together to make 25857 are 3 x 3 x 13 x 13 x 17. When we strip out the pairs only, we get 3 x 3 x 13 x 13 = 1521 and the square root of 1521 is 39. Therefore, A equals 39.

B = Divide 25857 by the number (A) squared. 39 squared is 1521 and 25857 divided by 1521 is 17. Therefore, B equals 17.

Once again we have A and B and can get our answer to 25857 in its simplest radical form as follows:

√25857 = A√B

√25857 = 39√17

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

Simplify Square Root of 25858
Here is the next square root on our list that we have simplifed for you.