Simplify Square Root of 18288

Here we will show you two methods that you can use to simplify the square root of 18288. In other words, we will show you how to find the square root of 18288 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.

√18288 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 18288 to simplify the square root of 18288. 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 18288. The factors of 18288 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 127, 144, 254, 381, 508, 762, 1016, 1143, 1524, 2032, 2286, 3048, 4572, 6096, 9144, and 18288. Furthermore, the greatest perfect square on this list is 144 and the square root of 144 is 12. Therefore, A equals 12.

B = Calculate 18288 divided by the greatest perfect square from the list of all factors of 18288. We determined above that the greatest perfect square from the list of all factors of 18288 is 144. Furthermore, 18288 divided by 144 is 127, therefore B equals 127.

Now we have A and B and can get our answer to 18288 in its simplest radical form as follows:

√18288 = A√B

√18288 = 12√127

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 18288 to simplify the square root of 18288 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 18288 and then take the square root of that product. The prime factors that multiply together to make 18288 are 2 x 2 x 2 x 2 x 3 x 3 x 127. 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 18288 by the number (A) squared. 12 squared is 144 and 18288 divided by 144 is 127. Therefore, B equals 127.

Once again we have A and B and can get our answer to 18288 in its simplest radical form as follows:

√18288 = A√B

√18288 = 12√127

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