Simplify Square Root of 48384

Here we will show you two methods that you can use to simplify the square root of 48384. In other words, we will show you how to find the square root of 48384 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.

√48384 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 48384 to simplify the square root of 48384. 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 48384. The factors of 48384 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 27, 28, 32, 36, 42, 48, 54, 56, 63, 64, 72, 84, 96, 108, 112, 126, 128, 144, 168, 189, 192, 216, 224, 252, 256, 288, 336, 378, 384, 432, 448, 504, 576, 672, 756, 768, 864, 896, 1008, 1152, 1344, 1512, 1728, 1792, 2016, 2304, 2688, 3024, 3456, 4032, 5376, 6048, 6912, 8064, 12096, 16128, 24192, and 48384. Furthermore, the greatest perfect square on this list is 2304 and the square root of 2304 is 48. Therefore, A equals 48.

B = Calculate 48384 divided by the greatest perfect square from the list of all factors of 48384. We determined above that the greatest perfect square from the list of all factors of 48384 is 2304. Furthermore, 48384 divided by 2304 is 21, therefore B equals 21.

Now we have A and B and can get our answer to 48384 in its simplest radical form as follows:

√48384 = A√B

√48384 = 48√21

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 48384 to simplify the square root of 48384 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 48384 and then take the square root of that product. The prime factors that multiply together to make 48384 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 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 48384 by the number (A) squared. 48 squared is 2304 and 48384 divided by 2304 is 21. Therefore, B equals 21.

Once again we have A and B and can get our answer to 48384 in its simplest radical form as follows:

√48384 = A√B

√48384 = 48√21

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