Simplify Square Root of 85833

Here we will show you two methods that you can use to simplify the square root of 85833. In other words, we will show you how to find the square root of 85833 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.

√85833 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 85833 to simplify the square root of 85833. 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 85833. The factors of 85833 are 1, 3, 9, 11, 17, 27, 33, 51, 99, 153, 187, 289, 297, 459, 561, 867, 1683, 2601, 3179, 5049, 7803, 9537, 28611, and 85833. Furthermore, the greatest perfect square on this list is 2601 and the square root of 2601 is 51. Therefore, A equals 51.

B = Calculate 85833 divided by the greatest perfect square from the list of all factors of 85833. We determined above that the greatest perfect square from the list of all factors of 85833 is 2601. Furthermore, 85833 divided by 2601 is 33, therefore B equals 33.

Now we have A and B and can get our answer to 85833 in its simplest radical form as follows:

√85833 = A√B

√85833 = 51√33

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 85833 to simplify the square root of 85833 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 85833 and then take the square root of that product. The prime factors that multiply together to make 85833 are 3 x 3 x 3 x 11 x 17 x 17. When we strip out the pairs only, we get 3 x 3 x 17 x 17 = 2601 and the square root of 2601 is 51. Therefore, A equals 51.

B = Divide 85833 by the number (A) squared. 51 squared is 2601 and 85833 divided by 2601 is 33. Therefore, B equals 33.

Once again we have A and B and can get our answer to 85833 in its simplest radical form as follows:

√85833 = A√B

√85833 = 51√33

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