Simplify Square Root of 54027

Here we will show you two methods that you can use to simplify the square root of 54027. In other words, we will show you how to find the square root of 54027 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.

√54027 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 54027 to simplify the square root of 54027. 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 54027. The factors of 54027 are 1, 3, 9, 23, 27, 29, 69, 81, 87, 207, 261, 621, 667, 783, 1863, 2001, 2349, 6003, 18009, and 54027. Furthermore, the greatest perfect square on this list is 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Calculate 54027 divided by the greatest perfect square from the list of all factors of 54027. We determined above that the greatest perfect square from the list of all factors of 54027 is 81. Furthermore, 54027 divided by 81 is 667, therefore B equals 667.

Now we have A and B and can get our answer to 54027 in its simplest radical form as follows:

√54027 = A√B

√54027 = 9√667

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 54027 to simplify the square root of 54027 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 54027 and then take the square root of that product. The prime factors that multiply together to make 54027 are 3 x 3 x 3 x 3 x 23 x 29. When we strip out the pairs only, we get 3 x 3 x 3 x 3 = 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Divide 54027 by the number (A) squared. 9 squared is 81 and 54027 divided by 81 is 667. Therefore, B equals 667.

Once again we have A and B and can get our answer to 54027 in its simplest radical form as follows:

√54027 = A√B

√54027 = 9√667

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Simplify Square Root of 54028
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