Simplify Square Root of 83205

Here we will show you two methods that you can use to simplify the square root of 83205. In other words, we will show you how to find the square root of 83205 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.

√83205 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 83205 to simplify the square root of 83205. 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 83205. The factors of 83205 are 1, 3, 5, 9, 15, 43, 45, 129, 215, 387, 645, 1849, 1935, 5547, 9245, 16641, 27735, and 83205. Furthermore, the greatest perfect square on this list is 16641 and the square root of 16641 is 129. Therefore, A equals 129.

B = Calculate 83205 divided by the greatest perfect square from the list of all factors of 83205. We determined above that the greatest perfect square from the list of all factors of 83205 is 16641. Furthermore, 83205 divided by 16641 is 5, therefore B equals 5.

Now we have A and B and can get our answer to 83205 in its simplest radical form as follows:

√83205 = A√B

√83205 = 129√5

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 83205 to simplify the square root of 83205 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 83205 and then take the square root of that product. The prime factors that multiply together to make 83205 are 3 x 3 x 5 x 43 x 43. When we strip out the pairs only, we get 3 x 3 x 43 x 43 = 16641 and the square root of 16641 is 129. Therefore, A equals 129.

B = Divide 83205 by the number (A) squared. 129 squared is 16641 and 83205 divided by 16641 is 5. Therefore, B equals 5.

Once again we have A and B and can get our answer to 83205 in its simplest radical form as follows:

√83205 = A√B

√83205 = 129√5

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Simplify Square Root of 83206
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