Simplify Square Root of 65688

Here we will show you two methods that you can use to simplify the square root of 65688. In other words, we will show you how to find the square root of 65688 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.

√65688 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 65688 to simplify the square root of 65688. 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 65688. The factors of 65688 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 17, 21, 23, 24, 28, 34, 42, 46, 51, 56, 68, 69, 84, 92, 102, 119, 136, 138, 161, 168, 184, 204, 238, 276, 322, 357, 391, 408, 476, 483, 552, 644, 714, 782, 952, 966, 1173, 1288, 1428, 1564, 1932, 2346, 2737, 2856, 3128, 3864, 4692, 5474, 8211, 9384, 10948, 16422, 21896, 32844, and 65688. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 65688 divided by the greatest perfect square from the list of all factors of 65688. We determined above that the greatest perfect square from the list of all factors of 65688 is 4. Furthermore, 65688 divided by 4 is 16422, therefore B equals 16422.

Now we have A and B and can get our answer to 65688 in its simplest radical form as follows:

√65688 = A√B

√65688 = 2√16422

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 65688 to simplify the square root of 65688 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 65688 and then take the square root of that product. The prime factors that multiply together to make 65688 are 2 x 2 x 2 x 3 x 7 x 17 x 23. When we strip out the pairs only, we get 2 x 2 = 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Divide 65688 by the number (A) squared. 2 squared is 4 and 65688 divided by 4 is 16422. Therefore, B equals 16422.

Once again we have A and B and can get our answer to 65688 in its simplest radical form as follows:

√65688 = A√B

√65688 = 2√16422

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