Simplify Square Root of 81328

Here we will show you two methods that you can use to simplify the square root of 81328. In other words, we will show you how to find the square root of 81328 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.

√81328 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 81328 to simplify the square root of 81328. 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 81328. The factors of 81328 are 1, 2, 4, 8, 13, 16, 17, 23, 26, 34, 46, 52, 68, 92, 104, 136, 184, 208, 221, 272, 299, 368, 391, 442, 598, 782, 884, 1196, 1564, 1768, 2392, 3128, 3536, 4784, 5083, 6256, 10166, 20332, 40664, and 81328. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 81328 divided by the greatest perfect square from the list of all factors of 81328. We determined above that the greatest perfect square from the list of all factors of 81328 is 16. Furthermore, 81328 divided by 16 is 5083, therefore B equals 5083.

Now we have A and B and can get our answer to 81328 in its simplest radical form as follows:

√81328 = A√B

√81328 = 4√5083

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 81328 to simplify the square root of 81328 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 81328 and then take the square root of that product. The prime factors that multiply together to make 81328 are 2 x 2 x 2 x 2 x 13 x 17 x 23. 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 81328 by the number (A) squared. 4 squared is 16 and 81328 divided by 16 is 5083. Therefore, B equals 5083.

Once again we have A and B and can get our answer to 81328 in its simplest radical form as follows:

√81328 = A√B

√81328 = 4√5083

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