Simplify Square Root of 69888

Here we will show you two methods that you can use to simplify the square root of 69888. In other words, we will show you how to find the square root of 69888 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.

√69888 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 69888 to simplify the square root of 69888. 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 69888. The factors of 69888 are 1, 2, 3, 4, 6, 7, 8, 12, 13, 14, 16, 21, 24, 26, 28, 32, 39, 42, 48, 52, 56, 64, 78, 84, 91, 96, 104, 112, 128, 156, 168, 182, 192, 208, 224, 256, 273, 312, 336, 364, 384, 416, 448, 546, 624, 672, 728, 768, 832, 896, 1092, 1248, 1344, 1456, 1664, 1792, 2184, 2496, 2688, 2912, 3328, 4368, 4992, 5376, 5824, 8736, 9984, 11648, 17472, 23296, 34944, and 69888. Furthermore, the greatest perfect square on this list is 256 and the square root of 256 is 16. Therefore, A equals 16.

B = Calculate 69888 divided by the greatest perfect square from the list of all factors of 69888. We determined above that the greatest perfect square from the list of all factors of 69888 is 256. Furthermore, 69888 divided by 256 is 273, therefore B equals 273.

Now we have A and B and can get our answer to 69888 in its simplest radical form as follows:

√69888 = A√B

√69888 = 16√273

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 69888 to simplify the square root of 69888 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 69888 and then take the square root of that product. The prime factors that multiply together to make 69888 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 7 x 13. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 256 and the square root of 256 is 16. Therefore, A equals 16.

B = Divide 69888 by the number (A) squared. 16 squared is 256 and 69888 divided by 256 is 273. Therefore, B equals 273.

Once again we have A and B and can get our answer to 69888 in its simplest radical form as follows:

√69888 = A√B

√69888 = 16√273

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