Simplify Square Root of 54784

Here we will show you two methods that you can use to simplify the square root of 54784. In other words, we will show you how to find the square root of 54784 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.

√54784 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 54784 to simplify the square root of 54784. 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 54784. The factors of 54784 are 1, 2, 4, 8, 16, 32, 64, 107, 128, 214, 256, 428, 512, 856, 1712, 3424, 6848, 13696, 27392, and 54784. Furthermore, the greatest perfect square on this list is 256 and the square root of 256 is 16. Therefore, A equals 16.

B = Calculate 54784 divided by the greatest perfect square from the list of all factors of 54784. We determined above that the greatest perfect square from the list of all factors of 54784 is 256. Furthermore, 54784 divided by 256 is 214, therefore B equals 214.

Now we have A and B and can get our answer to 54784 in its simplest radical form as follows:

√54784 = A√B

√54784 = 16√214

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 54784 to simplify the square root of 54784 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 54784 and then take the square root of that product. The prime factors that multiply together to make 54784 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 107. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 256 and the square root of 256 is 16. Therefore, A equals 16.

B = Divide 54784 by the number (A) squared. 16 squared is 256 and 54784 divided by 256 is 214. Therefore, B equals 214.

Once again we have A and B and can get our answer to 54784 in its simplest radical form as follows:

√54784 = A√B

√54784 = 16√214

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