Simplify Square Root of 19500

Here we will show you two methods that you can use to simplify the square root of 19500. In other words, we will show you how to find the square root of 19500 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.

√19500 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 19500 to simplify the square root of 19500. 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 19500. The factors of 19500 are 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 25, 26, 30, 39, 50, 52, 60, 65, 75, 78, 100, 125, 130, 150, 156, 195, 250, 260, 300, 325, 375, 390, 500, 650, 750, 780, 975, 1300, 1500, 1625, 1950, 3250, 3900, 4875, 6500, 9750, and 19500. Furthermore, the greatest perfect square on this list is 100 and the square root of 100 is 10. Therefore, A equals 10.

B = Calculate 19500 divided by the greatest perfect square from the list of all factors of 19500. We determined above that the greatest perfect square from the list of all factors of 19500 is 100. Furthermore, 19500 divided by 100 is 195, therefore B equals 195.

Now we have A and B and can get our answer to 19500 in its simplest radical form as follows:

√19500 = A√B

√19500 = 10√195

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 19500 to simplify the square root of 19500 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 19500 and then take the square root of that product. The prime factors that multiply together to make 19500 are 2 x 2 x 3 x 5 x 5 x 5 x 13. When we strip out the pairs only, we get 2 x 2 x 5 x 5 = 100 and the square root of 100 is 10. Therefore, A equals 10.

B = Divide 19500 by the number (A) squared. 10 squared is 100 and 19500 divided by 100 is 195. Therefore, B equals 195.

Once again we have A and B and can get our answer to 19500 in its simplest radical form as follows:

√19500 = A√B

√19500 = 10√195

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

Simplify Square Root of 19501
Here is the next square root on our list that we have simplifed for you.