Simplify Square Root of 22707

Here we will show you two methods that you can use to simplify the square root of 22707. In other words, we will show you how to find the square root of 22707 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.

√22707 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 22707 to simplify the square root of 22707. 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 22707. The factors of 22707 are 1, 3, 9, 27, 29, 87, 261, 783, 841, 2523, 7569, and 22707. Furthermore, the greatest perfect square on this list is 7569 and the square root of 7569 is 87. Therefore, A equals 87.

B = Calculate 22707 divided by the greatest perfect square from the list of all factors of 22707. We determined above that the greatest perfect square from the list of all factors of 22707 is 7569. Furthermore, 22707 divided by 7569 is 3, therefore B equals 3.

Now we have A and B and can get our answer to 22707 in its simplest radical form as follows:

√22707 = A√B

√22707 = 87√3

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 22707 to simplify the square root of 22707 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 22707 and then take the square root of that product. The prime factors that multiply together to make 22707 are 3 x 3 x 3 x 29 x 29. When we strip out the pairs only, we get 3 x 3 x 29 x 29 = 7569 and the square root of 7569 is 87. Therefore, A equals 87.

B = Divide 22707 by the number (A) squared. 87 squared is 7569 and 22707 divided by 7569 is 3. Therefore, B equals 3.

Once again we have A and B and can get our answer to 22707 in its simplest radical form as follows:

√22707 = A√B

√22707 = 87√3

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Simplify Square Root of 22708
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