Simplify Square Root of 27848

Here we will show you two methods that you can use to simplify the square root of 27848. In other words, we will show you how to find the square root of 27848 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.

√27848 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 27848 to simplify the square root of 27848. 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 27848. The factors of 27848 are 1, 2, 4, 8, 59, 118, 236, 472, 3481, 6962, 13924, and 27848. Furthermore, the greatest perfect square on this list is 13924 and the square root of 13924 is 118. Therefore, A equals 118.

B = Calculate 27848 divided by the greatest perfect square from the list of all factors of 27848. We determined above that the greatest perfect square from the list of all factors of 27848 is 13924. Furthermore, 27848 divided by 13924 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 27848 in its simplest radical form as follows:

√27848 = A√B

√27848 = 118√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 27848 to simplify the square root of 27848 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 27848 and then take the square root of that product. The prime factors that multiply together to make 27848 are 2 x 2 x 2 x 59 x 59. When we strip out the pairs only, we get 2 x 2 x 59 x 59 = 13924 and the square root of 13924 is 118. Therefore, A equals 118.

B = Divide 27848 by the number (A) squared. 118 squared is 13924 and 27848 divided by 13924 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 27848 in its simplest radical form as follows:

√27848 = A√B

√27848 = 118√2

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

Simplify Square Root of 27849
Here is the next square root on our list that we have simplifed for you.