Simplify Square Root of 57792

Here we will show you two methods that you can use to simplify the square root of 57792. In other words, we will show you how to find the square root of 57792 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.

√57792 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 57792 to simplify the square root of 57792. 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 57792. The factors of 57792 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 43, 48, 56, 64, 84, 86, 96, 112, 129, 168, 172, 192, 224, 258, 301, 336, 344, 448, 516, 602, 672, 688, 903, 1032, 1204, 1344, 1376, 1806, 2064, 2408, 2752, 3612, 4128, 4816, 7224, 8256, 9632, 14448, 19264, 28896, and 57792. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 57792 divided by the greatest perfect square from the list of all factors of 57792. We determined above that the greatest perfect square from the list of all factors of 57792 is 64. Furthermore, 57792 divided by 64 is 903, therefore B equals 903.

Now we have A and B and can get our answer to 57792 in its simplest radical form as follows:

√57792 = A√B

√57792 = 8√903

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 57792 to simplify the square root of 57792 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 57792 and then take the square root of that product. The prime factors that multiply together to make 57792 are 2 x 2 x 2 x 2 x 2 x 2 x 3 x 7 x 43. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 = 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Divide 57792 by the number (A) squared. 8 squared is 64 and 57792 divided by 64 is 903. Therefore, B equals 903.

Once again we have A and B and can get our answer to 57792 in its simplest radical form as follows:

√57792 = A√B

√57792 = 8√903

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Simplify Square Root of 57793
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