Simplify Square Root of 19404

Here we will show you two methods that you can use to simplify the square root of 19404. In other words, we will show you how to find the square root of 19404 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.

√19404 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 19404 to simplify the square root of 19404. 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 19404. The factors of 19404 are 1, 2, 3, 4, 6, 7, 9, 11, 12, 14, 18, 21, 22, 28, 33, 36, 42, 44, 49, 63, 66, 77, 84, 98, 99, 126, 132, 147, 154, 196, 198, 231, 252, 294, 308, 396, 441, 462, 539, 588, 693, 882, 924, 1078, 1386, 1617, 1764, 2156, 2772, 3234, 4851, 6468, 9702, and 19404. Furthermore, the greatest perfect square on this list is 1764 and the square root of 1764 is 42. Therefore, A equals 42.

B = Calculate 19404 divided by the greatest perfect square from the list of all factors of 19404. We determined above that the greatest perfect square from the list of all factors of 19404 is 1764. Furthermore, 19404 divided by 1764 is 11, therefore B equals 11.

Now we have A and B and can get our answer to 19404 in its simplest radical form as follows:

√19404 = A√B

√19404 = 42√11

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 19404 to simplify the square root of 19404 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 19404 and then take the square root of that product. The prime factors that multiply together to make 19404 are 2 x 2 x 3 x 3 x 7 x 7 x 11. When we strip out the pairs only, we get 2 x 2 x 3 x 3 x 7 x 7 = 1764 and the square root of 1764 is 42. Therefore, A equals 42.

B = Divide 19404 by the number (A) squared. 42 squared is 1764 and 19404 divided by 1764 is 11. Therefore, B equals 11.

Once again we have A and B and can get our answer to 19404 in its simplest radical form as follows:

√19404 = A√B

√19404 = 42√11

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