Simplify Square Root of 86227

Here we will show you two methods that you can use to simplify the square root of 86227. In other words, we will show you how to find the square root of 86227 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.

√86227 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 86227 to simplify the square root of 86227. 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 86227. The factors of 86227 are 1, 23, 163, 529, 3749, and 86227. Furthermore, the greatest perfect square on this list is 529 and the square root of 529 is 23. Therefore, A equals 23.

B = Calculate 86227 divided by the greatest perfect square from the list of all factors of 86227. We determined above that the greatest perfect square from the list of all factors of 86227 is 529. Furthermore, 86227 divided by 529 is 163, therefore B equals 163.

Now we have A and B and can get our answer to 86227 in its simplest radical form as follows:

√86227 = A√B

√86227 = 23√163

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 86227 to simplify the square root of 86227 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 86227 and then take the square root of that product. The prime factors that multiply together to make 86227 are 23 x 23 x 163. When we strip out the pairs only, we get 23 x 23 = 529 and the square root of 529 is 23. Therefore, A equals 23.

B = Divide 86227 by the number (A) squared. 23 squared is 529 and 86227 divided by 529 is 163. Therefore, B equals 163.

Once again we have A and B and can get our answer to 86227 in its simplest radical form as follows:

√86227 = A√B

√86227 = 23√163

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Simplify Square Root of 86228
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