Simplify Square Root of 54208

Here we will show you two methods that you can use to simplify the square root of 54208. In other words, we will show you how to find the square root of 54208 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.

√54208 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 54208 to simplify the square root of 54208. 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 54208. The factors of 54208 are 1, 2, 4, 7, 8, 11, 14, 16, 22, 28, 32, 44, 56, 64, 77, 88, 112, 121, 154, 176, 224, 242, 308, 352, 448, 484, 616, 704, 847, 968, 1232, 1694, 1936, 2464, 3388, 3872, 4928, 6776, 7744, 13552, 27104, and 54208. Furthermore, the greatest perfect square on this list is 7744 and the square root of 7744 is 88. Therefore, A equals 88.

B = Calculate 54208 divided by the greatest perfect square from the list of all factors of 54208. We determined above that the greatest perfect square from the list of all factors of 54208 is 7744. Furthermore, 54208 divided by 7744 is 7, therefore B equals 7.

Now we have A and B and can get our answer to 54208 in its simplest radical form as follows:

√54208 = A√B

√54208 = 88√7

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 54208 to simplify the square root of 54208 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 54208 and then take the square root of that product. The prime factors that multiply together to make 54208 are 2 x 2 x 2 x 2 x 2 x 2 x 7 x 11 x 11. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 11 x 11 = 7744 and the square root of 7744 is 88. Therefore, A equals 88.

B = Divide 54208 by the number (A) squared. 88 squared is 7744 and 54208 divided by 7744 is 7. Therefore, B equals 7.

Once again we have A and B and can get our answer to 54208 in its simplest radical form as follows:

√54208 = A√B

√54208 = 88√7

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