Simplify Square Root of 27648

Here we will show you two methods that you can use to simplify the square root of 27648. In other words, we will show you how to find the square root of 27648 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.

√27648 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 27648 to simplify the square root of 27648. 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 27648. The factors of 27648 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 128, 144, 192, 216, 256, 288, 384, 432, 512, 576, 768, 864, 1024, 1152, 1536, 1728, 2304, 3072, 3456, 4608, 6912, 9216, 13824, and 27648. Furthermore, the greatest perfect square on this list is 9216 and the square root of 9216 is 96. Therefore, A equals 96.

B = Calculate 27648 divided by the greatest perfect square from the list of all factors of 27648. We determined above that the greatest perfect square from the list of all factors of 27648 is 9216. Furthermore, 27648 divided by 9216 is 3, therefore B equals 3.

Now we have A and B and can get our answer to 27648 in its simplest radical form as follows:

√27648 = A√B

√27648 = 96√3

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 27648 to simplify the square root of 27648 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 27648 and then take the square root of that product. The prime factors that multiply together to make 27648 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 = 9216 and the square root of 9216 is 96. Therefore, A equals 96.

B = Divide 27648 by the number (A) squared. 96 squared is 9216 and 27648 divided by 9216 is 3. Therefore, B equals 3.

Once again we have A and B and can get our answer to 27648 in its simplest radical form as follows:

√27648 = A√B

√27648 = 96√3

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