Simplify Square Root of 55404

Here we will show you two methods that you can use to simplify the square root of 55404. In other words, we will show you how to find the square root of 55404 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.

√55404 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 55404 to simplify the square root of 55404. 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 55404. The factors of 55404 are 1, 2, 3, 4, 6, 9, 12, 18, 19, 27, 36, 38, 54, 57, 76, 81, 108, 114, 162, 171, 228, 243, 324, 342, 486, 513, 684, 729, 972, 1026, 1458, 1539, 2052, 2916, 3078, 4617, 6156, 9234, 13851, 18468, 27702, and 55404. Furthermore, the greatest perfect square on this list is 2916 and the square root of 2916 is 54. Therefore, A equals 54.

B = Calculate 55404 divided by the greatest perfect square from the list of all factors of 55404. We determined above that the greatest perfect square from the list of all factors of 55404 is 2916. Furthermore, 55404 divided by 2916 is 19, therefore B equals 19.

Now we have A and B and can get our answer to 55404 in its simplest radical form as follows:

√55404 = A√B

√55404 = 54√19

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 55404 to simplify the square root of 55404 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 55404 and then take the square root of that product. The prime factors that multiply together to make 55404 are 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3 x 19. When we strip out the pairs only, we get 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3 = 2916 and the square root of 2916 is 54. Therefore, A equals 54.

B = Divide 55404 by the number (A) squared. 54 squared is 2916 and 55404 divided by 2916 is 19. Therefore, B equals 19.

Once again we have A and B and can get our answer to 55404 in its simplest radical form as follows:

√55404 = A√B

√55404 = 54√19

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