Simplify Square Root of 54144

Here we will show you two methods that you can use to simplify the square root of 54144. In other words, we will show you how to find the square root of 54144 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.

√54144 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 54144 to simplify the square root of 54144. 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 54144. The factors of 54144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 47, 48, 64, 72, 94, 96, 128, 141, 144, 188, 192, 282, 288, 376, 384, 423, 564, 576, 752, 846, 1128, 1152, 1504, 1692, 2256, 3008, 3384, 4512, 6016, 6768, 9024, 13536, 18048, 27072, and 54144. Furthermore, the greatest perfect square on this list is 576 and the square root of 576 is 24. Therefore, A equals 24.

B = Calculate 54144 divided by the greatest perfect square from the list of all factors of 54144. We determined above that the greatest perfect square from the list of all factors of 54144 is 576. Furthermore, 54144 divided by 576 is 94, therefore B equals 94.

Now we have A and B and can get our answer to 54144 in its simplest radical form as follows:

√54144 = A√B

√54144 = 24√94

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 54144 to simplify the square root of 54144 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 54144 and then take the square root of that product. The prime factors that multiply together to make 54144 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 47. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 = 576 and the square root of 576 is 24. Therefore, A equals 24.

B = Divide 54144 by the number (A) squared. 24 squared is 576 and 54144 divided by 576 is 94. Therefore, B equals 94.

Once again we have A and B and can get our answer to 54144 in its simplest radical form as follows:

√54144 = A√B

√54144 = 24√94

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