Simplify Square Root of 19980

Here we will show you two methods that you can use to simplify the square root of 19980. In other words, we will show you how to find the square root of 19980 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.

√19980 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 19980 to simplify the square root of 19980. 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 19980. The factors of 19980 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 37, 45, 54, 60, 74, 90, 108, 111, 135, 148, 180, 185, 222, 270, 333, 370, 444, 540, 555, 666, 740, 999, 1110, 1332, 1665, 1998, 2220, 3330, 3996, 4995, 6660, 9990, and 19980. Furthermore, the greatest perfect square on this list is 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Calculate 19980 divided by the greatest perfect square from the list of all factors of 19980. We determined above that the greatest perfect square from the list of all factors of 19980 is 36. Furthermore, 19980 divided by 36 is 555, therefore B equals 555.

Now we have A and B and can get our answer to 19980 in its simplest radical form as follows:

√19980 = A√B

√19980 = 6√555

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 19980 to simplify the square root of 19980 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 19980 and then take the square root of that product. The prime factors that multiply together to make 19980 are 2 x 2 x 3 x 3 x 3 x 5 x 37. 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 19980 by the number (A) squared. 6 squared is 36 and 19980 divided by 36 is 555. Therefore, B equals 555.

Once again we have A and B and can get our answer to 19980 in its simplest radical form as follows:

√19980 = A√B

√19980 = 6√555

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

Simplify Square Root of 19981
Here is the next square root on our list that we have simplifed for you.