Simplify Square Root of 48552

Here we will show you two methods that you can use to simplify the square root of 48552. In other words, we will show you how to find the square root of 48552 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.

√48552 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 48552 to simplify the square root of 48552. 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 48552. The factors of 48552 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 17, 21, 24, 28, 34, 42, 51, 56, 68, 84, 102, 119, 136, 168, 204, 238, 289, 357, 408, 476, 578, 714, 867, 952, 1156, 1428, 1734, 2023, 2312, 2856, 3468, 4046, 6069, 6936, 8092, 12138, 16184, 24276, and 48552. Furthermore, the greatest perfect square on this list is 1156 and the square root of 1156 is 34. Therefore, A equals 34.

B = Calculate 48552 divided by the greatest perfect square from the list of all factors of 48552. We determined above that the greatest perfect square from the list of all factors of 48552 is 1156. Furthermore, 48552 divided by 1156 is 42, therefore B equals 42.

Now we have A and B and can get our answer to 48552 in its simplest radical form as follows:

√48552 = A√B

√48552 = 34√42

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 48552 to simplify the square root of 48552 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 48552 and then take the square root of that product. The prime factors that multiply together to make 48552 are 2 x 2 x 2 x 3 x 7 x 17 x 17. When we strip out the pairs only, we get 2 x 2 x 17 x 17 = 1156 and the square root of 1156 is 34. Therefore, A equals 34.

B = Divide 48552 by the number (A) squared. 34 squared is 1156 and 48552 divided by 1156 is 42. Therefore, B equals 42.

Once again we have A and B and can get our answer to 48552 in its simplest radical form as follows:

√48552 = A√B

√48552 = 34√42

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