Simplify Square Root of 32805

Here we will show you two methods that you can use to simplify the square root of 32805. In other words, we will show you how to find the square root of 32805 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.

√32805 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 32805 to simplify the square root of 32805. 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 32805. The factors of 32805 are 1, 3, 5, 9, 15, 27, 45, 81, 135, 243, 405, 729, 1215, 2187, 3645, 6561, 10935, and 32805. Furthermore, the greatest perfect square on this list is 6561 and the square root of 6561 is 81. Therefore, A equals 81.

B = Calculate 32805 divided by the greatest perfect square from the list of all factors of 32805. We determined above that the greatest perfect square from the list of all factors of 32805 is 6561. Furthermore, 32805 divided by 6561 is 5, therefore B equals 5.

Now we have A and B and can get our answer to 32805 in its simplest radical form as follows:

√32805 = A√B

√32805 = 81√5

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 32805 to simplify the square root of 32805 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 32805 and then take the square root of that product. The prime factors that multiply together to make 32805 are 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 5. When we strip out the pairs only, we get 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 = 6561 and the square root of 6561 is 81. Therefore, A equals 81.

B = Divide 32805 by the number (A) squared. 81 squared is 6561 and 32805 divided by 6561 is 5. Therefore, B equals 5.

Once again we have A and B and can get our answer to 32805 in its simplest radical form as follows:

√32805 = A√B

√32805 = 81√5

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Simplify Square Root of 32806
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