Simplify Square Root of 32256

Here we will show you two methods that you can use to simplify the square root of 32256. In other words, we will show you how to find the square root of 32256 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.

√32256 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 32256 to simplify the square root of 32256. 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 32256. The factors of 32256 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32, 36, 42, 48, 56, 63, 64, 72, 84, 96, 112, 126, 128, 144, 168, 192, 224, 252, 256, 288, 336, 384, 448, 504, 512, 576, 672, 768, 896, 1008, 1152, 1344, 1536, 1792, 2016, 2304, 2688, 3584, 4032, 4608, 5376, 8064, 10752, 16128, and 32256. Furthermore, the greatest perfect square on this list is 2304 and the square root of 2304 is 48. Therefore, A equals 48.

B = Calculate 32256 divided by the greatest perfect square from the list of all factors of 32256. We determined above that the greatest perfect square from the list of all factors of 32256 is 2304. Furthermore, 32256 divided by 2304 is 14, therefore B equals 14.

Now we have A and B and can get our answer to 32256 in its simplest radical form as follows:

√32256 = A√B

√32256 = 48√14

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 32256 to simplify the square root of 32256 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 32256 and then take the square root of that product. The prime factors that multiply together to make 32256 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 7. 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 3 x 3 = 2304 and the square root of 2304 is 48. Therefore, A equals 48.

B = Divide 32256 by the number (A) squared. 48 squared is 2304 and 32256 divided by 2304 is 14. Therefore, B equals 14.

Once again we have A and B and can get our answer to 32256 in its simplest radical form as follows:

√32256 = A√B

√32256 = 48√14

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