Simplify Square Root of 18144

Here we will show you two methods that you can use to simplify the square root of 18144. In other words, we will show you how to find the square root of 18144 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.

√18144 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 18144 to simplify the square root of 18144. 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 18144. The factors of 18144 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 27, 28, 32, 36, 42, 48, 54, 56, 63, 72, 81, 84, 96, 108, 112, 126, 144, 162, 168, 189, 216, 224, 252, 288, 324, 336, 378, 432, 504, 567, 648, 672, 756, 864, 1008, 1134, 1296, 1512, 2016, 2268, 2592, 3024, 4536, 6048, 9072, and 18144. Furthermore, the greatest perfect square on this list is 1296 and the square root of 1296 is 36. Therefore, A equals 36.

B = Calculate 18144 divided by the greatest perfect square from the list of all factors of 18144. We determined above that the greatest perfect square from the list of all factors of 18144 is 1296. Furthermore, 18144 divided by 1296 is 14, therefore B equals 14.

Now we have A and B and can get our answer to 18144 in its simplest radical form as follows:

√18144 = A√B

√18144 = 36√14

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 18144 to simplify the square root of 18144 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 18144 and then take the square root of that product. The prime factors that multiply together to make 18144 are 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 7. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 = 1296 and the square root of 1296 is 36. Therefore, A equals 36.

B = Divide 18144 by the number (A) squared. 36 squared is 1296 and 18144 divided by 1296 is 14. Therefore, B equals 14.

Once again we have A and B and can get our answer to 18144 in its simplest radical form as follows:

√18144 = A√B

√18144 = 36√14

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