Simplify Square Root of 81585

Here we will show you two methods that you can use to simplify the square root of 81585. In other words, we will show you how to find the square root of 81585 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.

√81585 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 81585 to simplify the square root of 81585. 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 81585. The factors of 81585 are 1, 3, 5, 7, 9, 15, 21, 35, 37, 45, 49, 63, 105, 111, 147, 185, 245, 259, 315, 333, 441, 555, 735, 777, 1295, 1665, 1813, 2205, 2331, 3885, 5439, 9065, 11655, 16317, 27195, and 81585. Furthermore, the greatest perfect square on this list is 441 and the square root of 441 is 21. Therefore, A equals 21.

B = Calculate 81585 divided by the greatest perfect square from the list of all factors of 81585. We determined above that the greatest perfect square from the list of all factors of 81585 is 441. Furthermore, 81585 divided by 441 is 185, therefore B equals 185.

Now we have A and B and can get our answer to 81585 in its simplest radical form as follows:

√81585 = A√B

√81585 = 21√185

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 81585 to simplify the square root of 81585 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 81585 and then take the square root of that product. The prime factors that multiply together to make 81585 are 3 x 3 x 5 x 7 x 7 x 37. When we strip out the pairs only, we get 3 x 3 x 7 x 7 = 441 and the square root of 441 is 21. Therefore, A equals 21.

B = Divide 81585 by the number (A) squared. 21 squared is 441 and 81585 divided by 441 is 185. Therefore, B equals 185.

Once again we have A and B and can get our answer to 81585 in its simplest radical form as follows:

√81585 = A√B

√81585 = 21√185

Simplify Square Root
Please enter another square root in the box below for us to simplify.

Simplify Square Root of 81586
Here is the next square root on our list that we have simplifed for you.