Simplify Square Root of 21800

Here we will show you two methods that you can use to simplify the square root of 21800. In other words, we will show you how to find the square root of 21800 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.

√21800 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 21800 to simplify the square root of 21800. 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 21800. The factors of 21800 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 109, 200, 218, 436, 545, 872, 1090, 2180, 2725, 4360, 5450, 10900, and 21800. Furthermore, the greatest perfect square on this list is 100 and the square root of 100 is 10. Therefore, A equals 10.

B = Calculate 21800 divided by the greatest perfect square from the list of all factors of 21800. We determined above that the greatest perfect square from the list of all factors of 21800 is 100. Furthermore, 21800 divided by 100 is 218, therefore B equals 218.

Now we have A and B and can get our answer to 21800 in its simplest radical form as follows:

√21800 = A√B

√21800 = 10√218

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 21800 to simplify the square root of 21800 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 21800 and then take the square root of that product. The prime factors that multiply together to make 21800 are 2 x 2 x 2 x 5 x 5 x 109. 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 21800 by the number (A) squared. 10 squared is 100 and 21800 divided by 100 is 218. Therefore, B equals 218.

Once again we have A and B and can get our answer to 21800 in its simplest radical form as follows:

√21800 = A√B

√21800 = 10√218

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

Simplify Square Root of 21801
Here is the next square root on our list that we have simplifed for you.