Simplify Square Root of 82256

Here we will show you two methods that you can use to simplify the square root of 82256. In other words, we will show you how to find the square root of 82256 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.

√82256 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 82256 to simplify the square root of 82256. 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 82256. The factors of 82256 are 1, 2, 4, 8, 16, 53, 97, 106, 194, 212, 388, 424, 776, 848, 1552, 5141, 10282, 20564, 41128, and 82256. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 82256 divided by the greatest perfect square from the list of all factors of 82256. We determined above that the greatest perfect square from the list of all factors of 82256 is 16. Furthermore, 82256 divided by 16 is 5141, therefore B equals 5141.

Now we have A and B and can get our answer to 82256 in its simplest radical form as follows:

√82256 = A√B

√82256 = 4√5141

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 82256 to simplify the square root of 82256 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 82256 and then take the square root of that product. The prime factors that multiply together to make 82256 are 2 x 2 x 2 x 2 x 53 x 97. When we strip out the pairs only, we get 2 x 2 x 2 x 2 = 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Divide 82256 by the number (A) squared. 4 squared is 16 and 82256 divided by 16 is 5141. Therefore, B equals 5141.

Once again we have A and B and can get our answer to 82256 in its simplest radical form as follows:

√82256 = A√B

√82256 = 4√5141

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Simplify Square Root of 82257
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