Simplify Square Root of 86528

Here we will show you two methods that you can use to simplify the square root of 86528. In other words, we will show you how to find the square root of 86528 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.

√86528 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 86528 to simplify the square root of 86528. 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 86528. The factors of 86528 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 169, 208, 256, 338, 416, 512, 676, 832, 1352, 1664, 2704, 3328, 5408, 6656, 10816, 21632, 43264, and 86528. Furthermore, the greatest perfect square on this list is 43264 and the square root of 43264 is 208. Therefore, A equals 208.

B = Calculate 86528 divided by the greatest perfect square from the list of all factors of 86528. We determined above that the greatest perfect square from the list of all factors of 86528 is 43264. Furthermore, 86528 divided by 43264 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 86528 in its simplest radical form as follows:

√86528 = A√B

√86528 = 208√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 86528 to simplify the square root of 86528 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 86528 and then take the square root of that product. The prime factors that multiply together to make 86528 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 13 x 13. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 13 x 13 = 43264 and the square root of 43264 is 208. Therefore, A equals 208.

B = Divide 86528 by the number (A) squared. 208 squared is 43264 and 86528 divided by 43264 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 86528 in its simplest radical form as follows:

√86528 = A√B

√86528 = 208√2

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