Simplify Square Root of 27048

Here we will show you two methods that you can use to simplify the square root of 27048. In other words, we will show you how to find the square root of 27048 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.

√27048 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 27048 to simplify the square root of 27048. 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 27048. The factors of 27048 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 23, 24, 28, 42, 46, 49, 56, 69, 84, 92, 98, 138, 147, 161, 168, 184, 196, 276, 294, 322, 392, 483, 552, 588, 644, 966, 1127, 1176, 1288, 1932, 2254, 3381, 3864, 4508, 6762, 9016, 13524, and 27048. Furthermore, the greatest perfect square on this list is 196 and the square root of 196 is 14. Therefore, A equals 14.

B = Calculate 27048 divided by the greatest perfect square from the list of all factors of 27048. We determined above that the greatest perfect square from the list of all factors of 27048 is 196. Furthermore, 27048 divided by 196 is 138, therefore B equals 138.

Now we have A and B and can get our answer to 27048 in its simplest radical form as follows:

√27048 = A√B

√27048 = 14√138

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 27048 to simplify the square root of 27048 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 27048 and then take the square root of that product. The prime factors that multiply together to make 27048 are 2 x 2 x 2 x 3 x 7 x 7 x 23. When we strip out the pairs only, we get 2 x 2 x 7 x 7 = 196 and the square root of 196 is 14. Therefore, A equals 14.

B = Divide 27048 by the number (A) squared. 14 squared is 196 and 27048 divided by 196 is 138. Therefore, B equals 138.

Once again we have A and B and can get our answer to 27048 in its simplest radical form as follows:

√27048 = A√B

√27048 = 14√138

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

Simplify Square Root of 27049
Here is the next square root on our list that we have simplifed for you.