Simplify Square Root of 19992

Here we will show you two methods that you can use to simplify the square root of 19992. In other words, we will show you how to find the square root of 19992 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.

√19992 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 19992 to simplify the square root of 19992. 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 19992. The factors of 19992 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 17, 21, 24, 28, 34, 42, 49, 51, 56, 68, 84, 98, 102, 119, 136, 147, 168, 196, 204, 238, 294, 357, 392, 408, 476, 588, 714, 833, 952, 1176, 1428, 1666, 2499, 2856, 3332, 4998, 6664, 9996, and 19992. Furthermore, the greatest perfect square on this list is 196 and the square root of 196 is 14. Therefore, A equals 14.

B = Calculate 19992 divided by the greatest perfect square from the list of all factors of 19992. We determined above that the greatest perfect square from the list of all factors of 19992 is 196. Furthermore, 19992 divided by 196 is 102, therefore B equals 102.

Now we have A and B and can get our answer to 19992 in its simplest radical form as follows:

√19992 = A√B

√19992 = 14√102

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 19992 to simplify the square root of 19992 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 19992 and then take the square root of that product. The prime factors that multiply together to make 19992 are 2 x 2 x 2 x 3 x 7 x 7 x 17. When we strip out the pairs only, we get 2 x 2 x 7 x 7 = 196 and the square root of 196 is 14. Therefore, A equals 14.

B = Divide 19992 by the number (A) squared. 14 squared is 196 and 19992 divided by 196 is 102. Therefore, B equals 102.

Once again we have A and B and can get our answer to 19992 in its simplest radical form as follows:

√19992 = A√B

√19992 = 14√102

Simplify Square Root
Please enter another square root in the box below for us to simplify.

Simplify Square Root of 19993
Here is the next square root on our list that we have simplifed for you.