Simplify Square Root of 19656

Here we will show you two methods that you can use to simplify the square root of 19656. In other words, we will show you how to find the square root of 19656 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.

√19656 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 19656 to simplify the square root of 19656. 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 19656. The factors of 19656 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 13, 14, 18, 21, 24, 26, 27, 28, 36, 39, 42, 52, 54, 56, 63, 72, 78, 84, 91, 104, 108, 117, 126, 156, 168, 182, 189, 216, 234, 252, 273, 312, 351, 364, 378, 468, 504, 546, 702, 728, 756, 819, 936, 1092, 1404, 1512, 1638, 2184, 2457, 2808, 3276, 4914, 6552, 9828, and 19656. Furthermore, the greatest perfect square on this list is 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Calculate 19656 divided by the greatest perfect square from the list of all factors of 19656. We determined above that the greatest perfect square from the list of all factors of 19656 is 36. Furthermore, 19656 divided by 36 is 546, therefore B equals 546.

Now we have A and B and can get our answer to 19656 in its simplest radical form as follows:

√19656 = A√B

√19656 = 6√546

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 19656 to simplify the square root of 19656 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 19656 and then take the square root of that product. The prime factors that multiply together to make 19656 are 2 x 2 x 2 x 3 x 3 x 3 x 7 x 13. When we strip out the pairs only, we get 2 x 2 x 3 x 3 = 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Divide 19656 by the number (A) squared. 6 squared is 36 and 19656 divided by 36 is 546. Therefore, B equals 546.

Once again we have A and B and can get our answer to 19656 in its simplest radical form as follows:

√19656 = A√B

√19656 = 6√546

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