Simplify Square Root of 22437

Here we will show you two methods that you can use to simplify the square root of 22437. In other words, we will show you how to find the square root of 22437 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.

√22437 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 22437 to simplify the square root of 22437. 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 22437. The factors of 22437 are 1, 3, 9, 27, 81, 277, 831, 2493, 7479, and 22437. Furthermore, the greatest perfect square on this list is 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Calculate 22437 divided by the greatest perfect square from the list of all factors of 22437. We determined above that the greatest perfect square from the list of all factors of 22437 is 81. Furthermore, 22437 divided by 81 is 277, therefore B equals 277.

Now we have A and B and can get our answer to 22437 in its simplest radical form as follows:

√22437 = A√B

√22437 = 9√277

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 22437 to simplify the square root of 22437 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 22437 and then take the square root of that product. The prime factors that multiply together to make 22437 are 3 x 3 x 3 x 3 x 277. When we strip out the pairs only, we get 3 x 3 x 3 x 3 = 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Divide 22437 by the number (A) squared. 9 squared is 81 and 22437 divided by 81 is 277. Therefore, B equals 277.

Once again we have A and B and can get our answer to 22437 in its simplest radical form as follows:

√22437 = A√B

√22437 = 9√277

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

Simplify Square Root of 22438
Here is the next square root on our list that we have simplifed for you.