Simplify Square Root of 83376

Here we will show you two methods that you can use to simplify the square root of 83376. In other words, we will show you how to find the square root of 83376 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.

√83376 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 83376 to simplify the square root of 83376. 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 83376. The factors of 83376 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 193, 216, 386, 432, 579, 772, 1158, 1544, 1737, 2316, 3088, 3474, 4632, 5211, 6948, 9264, 10422, 13896, 20844, 27792, 41688, and 83376. Furthermore, the greatest perfect square on this list is 144 and the square root of 144 is 12. Therefore, A equals 12.

B = Calculate 83376 divided by the greatest perfect square from the list of all factors of 83376. We determined above that the greatest perfect square from the list of all factors of 83376 is 144. Furthermore, 83376 divided by 144 is 579, therefore B equals 579.

Now we have A and B and can get our answer to 83376 in its simplest radical form as follows:

√83376 = A√B

√83376 = 12√579

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 83376 to simplify the square root of 83376 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 83376 and then take the square root of that product. The prime factors that multiply together to make 83376 are 2 x 2 x 2 x 2 x 3 x 3 x 3 x 193. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 3 x 3 = 144 and the square root of 144 is 12. Therefore, A equals 12.

B = Divide 83376 by the number (A) squared. 12 squared is 144 and 83376 divided by 144 is 579. Therefore, B equals 579.

Once again we have A and B and can get our answer to 83376 in its simplest radical form as follows:

√83376 = A√B

√83376 = 12√579

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