Simplify Square Root of 72912

Here we will show you two methods that you can use to simplify the square root of 72912. In other words, we will show you how to find the square root of 72912 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.

√72912 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 72912 to simplify the square root of 72912. 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 72912. The factors of 72912 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 31, 42, 48, 49, 56, 62, 84, 93, 98, 112, 124, 147, 168, 186, 196, 217, 248, 294, 336, 372, 392, 434, 496, 588, 651, 744, 784, 868, 1176, 1302, 1488, 1519, 1736, 2352, 2604, 3038, 3472, 4557, 5208, 6076, 9114, 10416, 12152, 18228, 24304, 36456, and 72912. Furthermore, the greatest perfect square on this list is 784 and the square root of 784 is 28. Therefore, A equals 28.

B = Calculate 72912 divided by the greatest perfect square from the list of all factors of 72912. We determined above that the greatest perfect square from the list of all factors of 72912 is 784. Furthermore, 72912 divided by 784 is 93, therefore B equals 93.

Now we have A and B and can get our answer to 72912 in its simplest radical form as follows:

√72912 = A√B

√72912 = 28√93

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 72912 to simplify the square root of 72912 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 72912 and then take the square root of that product. The prime factors that multiply together to make 72912 are 2 x 2 x 2 x 2 x 3 x 7 x 7 x 31. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 7 x 7 = 784 and the square root of 784 is 28. Therefore, A equals 28.

B = Divide 72912 by the number (A) squared. 28 squared is 784 and 72912 divided by 784 is 93. Therefore, B equals 93.

Once again we have A and B and can get our answer to 72912 in its simplest radical form as follows:

√72912 = A√B

√72912 = 28√93

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