Simplify Square Root of 22716

Here we will show you two methods that you can use to simplify the square root of 22716. In other words, we will show you how to find the square root of 22716 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.

√22716 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 22716 to simplify the square root of 22716. 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 22716. The factors of 22716 are 1, 2, 3, 4, 6, 9, 12, 18, 36, 631, 1262, 1893, 2524, 3786, 5679, 7572, 11358, and 22716. Furthermore, the greatest perfect square on this list is 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Calculate 22716 divided by the greatest perfect square from the list of all factors of 22716. We determined above that the greatest perfect square from the list of all factors of 22716 is 36. Furthermore, 22716 divided by 36 is 631, therefore B equals 631.

Now we have A and B and can get our answer to 22716 in its simplest radical form as follows:

√22716 = A√B

√22716 = 6√631

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 22716 to simplify the square root of 22716 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 22716 and then take the square root of that product. The prime factors that multiply together to make 22716 are 2 x 2 x 3 x 3 x 631. When we strip out the pairs only, we get 2 x 2 x 3 x 3 = 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Divide 22716 by the number (A) squared. 6 squared is 36 and 22716 divided by 36 is 631. Therefore, B equals 631.

Once again we have A and B and can get our answer to 22716 in its simplest radical form as follows:

√22716 = A√B

√22716 = 6√631

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Simplify Square Root of 22717
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