Here we will show you two methods that you can use to simplify the square root of 22001. In other words, we will show you how to find the square root of 22001 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.

√22001 = A√B

**Greatest Perfect Square Factor Method**

The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 22001 to simplify the square root of 22001. 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 22001. The factors of 22001 are 1, 7, 49, 449, 3143, and 22001. Furthermore, the greatest perfect square on this list is 49 and the square root of 49 is 7. Therefore, A equals 7.

**B**= Calculate 22001 divided by the greatest perfect square from the list of all factors of 22001. We determined above that the greatest perfect square from the list of all factors of 22001 is 49. Furthermore, 22001 divided by 49 is 449, therefore B equals 449.

Now we have A and B and can get our answer to 22001 in its simplest radical form as follows:

√22001 = A√B

**√22001 = 7√449**

**Double Prime Factor Method**

The Double Prime Factor Method uses the prime factors of 22001 to simplify the square root of 22001 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 22001 and then take the square root of that product. The prime factors that multiply together to make 22001 are 7 x 7 x 449. When we strip out the pairs only, we get 7 x 7 = 49 and the square root of 49 is 7. Therefore, A equals 7.

**B**= Divide 22001 by the number (A) squared. 7 squared is 49 and 22001 divided by 49 is 449. Therefore, B equals 449.

Once again we have A and B and can get our answer to 22001 in its simplest radical form as follows:

√22001 = A√B

**√22001 = 7√449**

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