Simplify Square Root of 85698

Here we will show you two methods that you can use to simplify the square root of 85698. In other words, we will show you how to find the square root of 85698 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.

√85698 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 85698 to simplify the square root of 85698. 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 85698. The factors of 85698 are 1, 2, 3, 6, 9, 18, 23, 27, 46, 54, 69, 81, 138, 162, 207, 414, 529, 621, 1058, 1242, 1587, 1863, 3174, 3726, 4761, 9522, 14283, 28566, 42849, and 85698. Furthermore, the greatest perfect square on this list is 42849 and the square root of 42849 is 207. Therefore, A equals 207.

B = Calculate 85698 divided by the greatest perfect square from the list of all factors of 85698. We determined above that the greatest perfect square from the list of all factors of 85698 is 42849. Furthermore, 85698 divided by 42849 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 85698 in its simplest radical form as follows:

√85698 = A√B

√85698 = 207√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 85698 to simplify the square root of 85698 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 85698 and then take the square root of that product. The prime factors that multiply together to make 85698 are 2 x 3 x 3 x 3 x 3 x 23 x 23. When we strip out the pairs only, we get 3 x 3 x 3 x 3 x 23 x 23 = 42849 and the square root of 42849 is 207. Therefore, A equals 207.

B = Divide 85698 by the number (A) squared. 207 squared is 42849 and 85698 divided by 42849 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 85698 in its simplest radical form as follows:

√85698 = A√B

√85698 = 207√2

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