Simplify Square Root of 19764

Here we will show you two methods that you can use to simplify the square root of 19764. In other words, we will show you how to find the square root of 19764 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.

√19764 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 19764 to simplify the square root of 19764. 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 19764. The factors of 19764 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 61, 81, 108, 122, 162, 183, 244, 324, 366, 549, 732, 1098, 1647, 2196, 3294, 4941, 6588, 9882, and 19764. Furthermore, the greatest perfect square on this list is 324 and the square root of 324 is 18. Therefore, A equals 18.

B = Calculate 19764 divided by the greatest perfect square from the list of all factors of 19764. We determined above that the greatest perfect square from the list of all factors of 19764 is 324. Furthermore, 19764 divided by 324 is 61, therefore B equals 61.

Now we have A and B and can get our answer to 19764 in its simplest radical form as follows:

√19764 = A√B

√19764 = 18√61

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 19764 to simplify the square root of 19764 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 19764 and then take the square root of that product. The prime factors that multiply together to make 19764 are 2 x 2 x 3 x 3 x 3 x 3 x 61. When we strip out the pairs only, we get 2 x 2 x 3 x 3 x 3 x 3 = 324 and the square root of 324 is 18. Therefore, A equals 18.

B = Divide 19764 by the number (A) squared. 18 squared is 324 and 19764 divided by 324 is 61. Therefore, B equals 61.

Once again we have A and B and can get our answer to 19764 in its simplest radical form as follows:

√19764 = A√B

√19764 = 18√61

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