Simplify Square Root of 85683

Here we will show you two methods that you can use to simplify the square root of 85683. In other words, we will show you how to find the square root of 85683 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.

√85683 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 85683 to simplify the square root of 85683. 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 85683. The factors of 85683 are 1, 3, 13, 39, 169, 507, 2197, 6591, 28561, and 85683. Furthermore, the greatest perfect square on this list is 28561 and the square root of 28561 is 169. Therefore, A equals 169.

B = Calculate 85683 divided by the greatest perfect square from the list of all factors of 85683. We determined above that the greatest perfect square from the list of all factors of 85683 is 28561. Furthermore, 85683 divided by 28561 is 3, therefore B equals 3.

Now we have A and B and can get our answer to 85683 in its simplest radical form as follows:

√85683 = A√B

√85683 = 169√3

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 85683 to simplify the square root of 85683 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 85683 and then take the square root of that product. The prime factors that multiply together to make 85683 are 3 x 13 x 13 x 13 x 13. When we strip out the pairs only, we get 13 x 13 x 13 x 13 = 28561 and the square root of 28561 is 169. Therefore, A equals 169.

B = Divide 85683 by the number (A) squared. 169 squared is 28561 and 85683 divided by 28561 is 3. Therefore, B equals 3.

Once again we have A and B and can get our answer to 85683 in its simplest radical form as follows:

√85683 = A√B

√85683 = 169√3

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Simplify Square Root of 85684
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