Simplify Square Root of 18576

Here we will show you two methods that you can use to simplify the square root of 18576. In other words, we will show you how to find the square root of 18576 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.

√18576 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 18576 to simplify the square root of 18576. 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 18576. The factors of 18576 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 43, 48, 54, 72, 86, 108, 129, 144, 172, 216, 258, 344, 387, 432, 516, 688, 774, 1032, 1161, 1548, 2064, 2322, 3096, 4644, 6192, 9288, and 18576. Furthermore, the greatest perfect square on this list is 144 and the square root of 144 is 12. Therefore, A equals 12.

B = Calculate 18576 divided by the greatest perfect square from the list of all factors of 18576. We determined above that the greatest perfect square from the list of all factors of 18576 is 144. Furthermore, 18576 divided by 144 is 129, therefore B equals 129.

Now we have A and B and can get our answer to 18576 in its simplest radical form as follows:

√18576 = A√B

√18576 = 12√129

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 18576 to simplify the square root of 18576 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 18576 and then take the square root of that product. The prime factors that multiply together to make 18576 are 2 x 2 x 2 x 2 x 3 x 3 x 3 x 43. 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 18576 by the number (A) squared. 12 squared is 144 and 18576 divided by 144 is 129. Therefore, B equals 129.

Once again we have A and B and can get our answer to 18576 in its simplest radical form as follows:

√18576 = A√B

√18576 = 12√129

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