Simplify Square Root of 72576

Here we will show you two methods that you can use to simplify the square root of 72576. In other words, we will show you how to find the square root of 72576 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.

√72576 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 72576 to simplify the square root of 72576. 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 72576. The factors of 72576 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, 81, 84, 96, 108, 112, 126, 128, 144, 162, 168, 189, 192, 216, 224, 252, 288, 324, 336, 378, 384, 432, 448, 504, 567, 576, 648, 672, 756, 864, 896, 1008, 1134, 1152, 1296, 1344, 1512, 1728, 2016, 2268, 2592, 2688, 3024, 3456, 4032, 4536, 5184, 6048, 8064, 9072, 10368, 12096, 18144, 24192, 36288, and 72576. Furthermore, the greatest perfect square on this list is 5184 and the square root of 5184 is 72. Therefore, A equals 72.

B = Calculate 72576 divided by the greatest perfect square from the list of all factors of 72576. We determined above that the greatest perfect square from the list of all factors of 72576 is 5184. Furthermore, 72576 divided by 5184 is 14, therefore B equals 14.

Now we have A and B and can get our answer to 72576 in its simplest radical form as follows:

√72576 = A√B

√72576 = 72√14

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 72576 to simplify the square root of 72576 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 72576 and then take the square root of that product. The prime factors that multiply together to make 72576 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 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 3 x 3 x 3 x 3 = 5184 and the square root of 5184 is 72. Therefore, A equals 72.

B = Divide 72576 by the number (A) squared. 72 squared is 5184 and 72576 divided by 5184 is 14. Therefore, B equals 14.

Once again we have A and B and can get our answer to 72576 in its simplest radical form as follows:

√72576 = A√B

√72576 = 72√14

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Simplify Square Root of 72577
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