Simplify Square Root of 54768

Here we will show you two methods that you can use to simplify the square root of 54768. In other words, we will show you how to find the square root of 54768 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.

√54768 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 54768 to simplify the square root of 54768. 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 54768. The factors of 54768 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 163, 168, 326, 336, 489, 652, 978, 1141, 1304, 1956, 2282, 2608, 3423, 3912, 4564, 6846, 7824, 9128, 13692, 18256, 27384, and 54768. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 54768 divided by the greatest perfect square from the list of all factors of 54768. We determined above that the greatest perfect square from the list of all factors of 54768 is 16. Furthermore, 54768 divided by 16 is 3423, therefore B equals 3423.

Now we have A and B and can get our answer to 54768 in its simplest radical form as follows:

√54768 = A√B

√54768 = 4√3423

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 54768 to simplify the square root of 54768 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 54768 and then take the square root of that product. The prime factors that multiply together to make 54768 are 2 x 2 x 2 x 2 x 3 x 7 x 163. When we strip out the pairs only, we get 2 x 2 x 2 x 2 = 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Divide 54768 by the number (A) squared. 4 squared is 16 and 54768 divided by 16 is 3423. Therefore, B equals 3423.

Once again we have A and B and can get our answer to 54768 in its simplest radical form as follows:

√54768 = A√B

√54768 = 4√3423

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