Simplify Square Root of 39900

Here we will show you two methods that you can use to simplify the square root of 39900. In other words, we will show you how to find the square root of 39900 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.

√39900 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 39900 to simplify the square root of 39900. 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 39900. The factors of 39900 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 19, 20, 21, 25, 28, 30, 35, 38, 42, 50, 57, 60, 70, 75, 76, 84, 95, 100, 105, 114, 133, 140, 150, 175, 190, 210, 228, 266, 285, 300, 350, 380, 399, 420, 475, 525, 532, 570, 665, 700, 798, 950, 1050, 1140, 1330, 1425, 1596, 1900, 1995, 2100, 2660, 2850, 3325, 3990, 5700, 6650, 7980, 9975, 13300, 19950, and 39900. Furthermore, the greatest perfect square on this list is 100 and the square root of 100 is 10. Therefore, A equals 10.

B = Calculate 39900 divided by the greatest perfect square from the list of all factors of 39900. We determined above that the greatest perfect square from the list of all factors of 39900 is 100. Furthermore, 39900 divided by 100 is 399, therefore B equals 399.

Now we have A and B and can get our answer to 39900 in its simplest radical form as follows:

√39900 = A√B

√39900 = 10√399

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 39900 to simplify the square root of 39900 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 39900 and then take the square root of that product. The prime factors that multiply together to make 39900 are 2 x 2 x 3 x 5 x 5 x 7 x 19. 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 39900 by the number (A) squared. 10 squared is 100 and 39900 divided by 100 is 399. Therefore, B equals 399.

Once again we have A and B and can get our answer to 39900 in its simplest radical form as follows:

√39900 = A√B

√39900 = 10√399

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

Simplify Square Root of 39901
Here is the next square root on our list that we have simplifed for you.