Simplify Square Root of 56628

Here we will show you two methods that you can use to simplify the square root of 56628. In other words, we will show you how to find the square root of 56628 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.

√56628 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 56628 to simplify the square root of 56628. 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 56628. The factors of 56628 are 1, 2, 3, 4, 6, 9, 11, 12, 13, 18, 22, 26, 33, 36, 39, 44, 52, 66, 78, 99, 117, 121, 132, 143, 156, 198, 234, 242, 286, 363, 396, 429, 468, 484, 572, 726, 858, 1089, 1287, 1452, 1573, 1716, 2178, 2574, 3146, 4356, 4719, 5148, 6292, 9438, 14157, 18876, 28314, and 56628. Furthermore, the greatest perfect square on this list is 4356 and the square root of 4356 is 66. Therefore, A equals 66.

B = Calculate 56628 divided by the greatest perfect square from the list of all factors of 56628. We determined above that the greatest perfect square from the list of all factors of 56628 is 4356. Furthermore, 56628 divided by 4356 is 13, therefore B equals 13.

Now we have A and B and can get our answer to 56628 in its simplest radical form as follows:

√56628 = A√B

√56628 = 66√13

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 56628 to simplify the square root of 56628 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 56628 and then take the square root of that product. The prime factors that multiply together to make 56628 are 2 x 2 x 3 x 3 x 11 x 11 x 13. When we strip out the pairs only, we get 2 x 2 x 3 x 3 x 11 x 11 = 4356 and the square root of 4356 is 66. Therefore, A equals 66.

B = Divide 56628 by the number (A) squared. 66 squared is 4356 and 56628 divided by 4356 is 13. Therefore, B equals 13.

Once again we have A and B and can get our answer to 56628 in its simplest radical form as follows:

√56628 = A√B

√56628 = 66√13

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