Simplify Square Root of 81872

Here we will show you two methods that you can use to simplify the square root of 81872. In other words, we will show you how to find the square root of 81872 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.

√81872 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 81872 to simplify the square root of 81872. 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 81872. The factors of 81872 are 1, 2, 4, 7, 8, 14, 16, 17, 28, 34, 43, 56, 68, 86, 112, 119, 136, 172, 238, 272, 301, 344, 476, 602, 688, 731, 952, 1204, 1462, 1904, 2408, 2924, 4816, 5117, 5848, 10234, 11696, 20468, 40936, and 81872. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 81872 divided by the greatest perfect square from the list of all factors of 81872. We determined above that the greatest perfect square from the list of all factors of 81872 is 16. Furthermore, 81872 divided by 16 is 5117, therefore B equals 5117.

Now we have A and B and can get our answer to 81872 in its simplest radical form as follows:

√81872 = A√B

√81872 = 4√5117

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 81872 to simplify the square root of 81872 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 81872 and then take the square root of that product. The prime factors that multiply together to make 81872 are 2 x 2 x 2 x 2 x 7 x 17 x 43. When we strip out the pairs only, we get 2 x 2 x 2 x 2 = 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Divide 81872 by the number (A) squared. 4 squared is 16 and 81872 divided by 16 is 5117. Therefore, B equals 5117.

Once again we have A and B and can get our answer to 81872 in its simplest radical form as follows:

√81872 = A√B

√81872 = 4√5117

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