Simplify Square Root of 85671

Here we will show you two methods that you can use to simplify the square root of 85671. In other words, we will show you how to find the square root of 85671 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.

√85671 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 85671 to simplify the square root of 85671. 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 85671. The factors of 85671 are 1, 3, 9, 19, 27, 57, 167, 171, 501, 513, 1503, 3173, 4509, 9519, 28557, and 85671. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 85671 divided by the greatest perfect square from the list of all factors of 85671. We determined above that the greatest perfect square from the list of all factors of 85671 is 9. Furthermore, 85671 divided by 9 is 9519, therefore B equals 9519.

Now we have A and B and can get our answer to 85671 in its simplest radical form as follows:

√85671 = A√B

√85671 = 3√9519

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 85671 to simplify the square root of 85671 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 85671 and then take the square root of that product. The prime factors that multiply together to make 85671 are 3 x 3 x 3 x 19 x 167. When we strip out the pairs only, we get 3 x 3 = 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Divide 85671 by the number (A) squared. 3 squared is 9 and 85671 divided by 9 is 9519. Therefore, B equals 9519.

Once again we have A and B and can get our answer to 85671 in its simplest radical form as follows:

√85671 = A√B

√85671 = 3√9519

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Simplify Square Root of 85672
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