Simplify Square Root of 81360

Here we will show you two methods that you can use to simplify the square root of 81360. In other words, we will show you how to find the square root of 81360 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.

√81360 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 81360 to simplify the square root of 81360. 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 81360. The factors of 81360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 113, 120, 144, 180, 226, 240, 339, 360, 452, 565, 678, 720, 904, 1017, 1130, 1356, 1695, 1808, 2034, 2260, 2712, 3390, 4068, 4520, 5085, 5424, 6780, 8136, 9040, 10170, 13560, 16272, 20340, 27120, 40680, and 81360. Furthermore, the greatest perfect square on this list is 144 and the square root of 144 is 12. Therefore, A equals 12.

B = Calculate 81360 divided by the greatest perfect square from the list of all factors of 81360. We determined above that the greatest perfect square from the list of all factors of 81360 is 144. Furthermore, 81360 divided by 144 is 565, therefore B equals 565.

Now we have A and B and can get our answer to 81360 in its simplest radical form as follows:

√81360 = A√B

√81360 = 12√565

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 81360 to simplify the square root of 81360 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 81360 and then take the square root of that product. The prime factors that multiply together to make 81360 are 2 x 2 x 2 x 2 x 3 x 3 x 5 x 113. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 3 x 3 = 144 and the square root of 144 is 12. Therefore, A equals 12.

B = Divide 81360 by the number (A) squared. 12 squared is 144 and 81360 divided by 144 is 565. Therefore, B equals 565.

Once again we have A and B and can get our answer to 81360 in its simplest radical form as follows:

√81360 = A√B

√81360 = 12√565

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