Simplify Square Root of 82432

Here we will show you two methods that you can use to simplify the square root of 82432. In other words, we will show you how to find the square root of 82432 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.

√82432 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 82432 to simplify the square root of 82432. 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 82432. The factors of 82432 are 1, 2, 4, 7, 8, 14, 16, 23, 28, 32, 46, 56, 64, 92, 112, 128, 161, 184, 224, 256, 322, 368, 448, 512, 644, 736, 896, 1288, 1472, 1792, 2576, 2944, 3584, 5152, 5888, 10304, 11776, 20608, 41216, and 82432. Furthermore, the greatest perfect square on this list is 256 and the square root of 256 is 16. Therefore, A equals 16.

B = Calculate 82432 divided by the greatest perfect square from the list of all factors of 82432. We determined above that the greatest perfect square from the list of all factors of 82432 is 256. Furthermore, 82432 divided by 256 is 322, therefore B equals 322.

Now we have A and B and can get our answer to 82432 in its simplest radical form as follows:

√82432 = A√B

√82432 = 16√322

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 82432 to simplify the square root of 82432 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 82432 and then take the square root of that product. The prime factors that multiply together to make 82432 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 7 x 23. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 256 and the square root of 256 is 16. Therefore, A equals 16.

B = Divide 82432 by the number (A) squared. 16 squared is 256 and 82432 divided by 256 is 322. Therefore, B equals 322.

Once again we have A and B and can get our answer to 82432 in its simplest radical form as follows:

√82432 = A√B

√82432 = 16√322

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