Simplify Square Root of 55296

Here we will show you two methods that you can use to simplify the square root of 55296. In other words, we will show you how to find the square root of 55296 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.

√55296 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 55296 to simplify the square root of 55296. 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 55296. The factors of 55296 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, 2048, 2304, 3072, 3456, 4608, 6144, 6912, 9216, 13824, 18432, 27648, and 55296. Furthermore, the greatest perfect square on this list is 9216 and the square root of 9216 is 96. Therefore, A equals 96.

B = Calculate 55296 divided by the greatest perfect square from the list of all factors of 55296. We determined above that the greatest perfect square from the list of all factors of 55296 is 9216. Furthermore, 55296 divided by 9216 is 6, therefore B equals 6.

Now we have A and B and can get our answer to 55296 in its simplest radical form as follows:

√55296 = A√B

√55296 = 96√6

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 55296 to simplify the square root of 55296 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 55296 and then take the square root of that product. The prime factors that multiply together to make 55296 are 2 x 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 55296 by the number (A) squared. 96 squared is 9216 and 55296 divided by 9216 is 6. Therefore, B equals 6.

Once again we have A and B and can get our answer to 55296 in its simplest radical form as follows:

√55296 = A√B

√55296 = 96√6

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