Simplify Square Root of 54096

Here we will show you two methods that you can use to simplify the square root of 54096. In other words, we will show you how to find the square root of 54096 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.

√54096 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 54096 to simplify the square root of 54096. 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 54096. The factors of 54096 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 23, 24, 28, 42, 46, 48, 49, 56, 69, 84, 92, 98, 112, 138, 147, 161, 168, 184, 196, 276, 294, 322, 336, 368, 392, 483, 552, 588, 644, 784, 966, 1104, 1127, 1176, 1288, 1932, 2254, 2352, 2576, 3381, 3864, 4508, 6762, 7728, 9016, 13524, 18032, 27048, and 54096. Furthermore, the greatest perfect square on this list is 784 and the square root of 784 is 28. Therefore, A equals 28.

B = Calculate 54096 divided by the greatest perfect square from the list of all factors of 54096. We determined above that the greatest perfect square from the list of all factors of 54096 is 784. Furthermore, 54096 divided by 784 is 69, therefore B equals 69.

Now we have A and B and can get our answer to 54096 in its simplest radical form as follows:

√54096 = A√B

√54096 = 28√69

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 54096 to simplify the square root of 54096 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 54096 and then take the square root of that product. The prime factors that multiply together to make 54096 are 2 x 2 x 2 x 2 x 3 x 7 x 7 x 23. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 7 x 7 = 784 and the square root of 784 is 28. Therefore, A equals 28.

B = Divide 54096 by the number (A) squared. 28 squared is 784 and 54096 divided by 784 is 69. Therefore, B equals 69.

Once again we have A and B and can get our answer to 54096 in its simplest radical form as follows:

√54096 = A√B

√54096 = 28√69

Simplify Square Root
Please enter another square root in the box below for us to simplify.

Simplify Square Root of 54097
Here is the next square root on our list that we have simplifed for you.