Simplify Square Root of 22264

Here we will show you two methods that you can use to simplify the square root of 22264. In other words, we will show you how to find the square root of 22264 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.

√22264 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 22264 to simplify the square root of 22264. 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 22264. The factors of 22264 are 1, 2, 4, 8, 11, 22, 23, 44, 46, 88, 92, 121, 184, 242, 253, 484, 506, 968, 1012, 2024, 2783, 5566, 11132, and 22264. Furthermore, the greatest perfect square on this list is 484 and the square root of 484 is 22. Therefore, A equals 22.

B = Calculate 22264 divided by the greatest perfect square from the list of all factors of 22264. We determined above that the greatest perfect square from the list of all factors of 22264 is 484. Furthermore, 22264 divided by 484 is 46, therefore B equals 46.

Now we have A and B and can get our answer to 22264 in its simplest radical form as follows:

√22264 = A√B

√22264 = 22√46

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 22264 to simplify the square root of 22264 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 22264 and then take the square root of that product. The prime factors that multiply together to make 22264 are 2 x 2 x 2 x 11 x 11 x 23. When we strip out the pairs only, we get 2 x 2 x 11 x 11 = 484 and the square root of 484 is 22. Therefore, A equals 22.

B = Divide 22264 by the number (A) squared. 22 squared is 484 and 22264 divided by 484 is 46. Therefore, B equals 46.

Once again we have A and B and can get our answer to 22264 in its simplest radical form as follows:

√22264 = A√B

√22264 = 22√46

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Simplify Square Root of 22265
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