Simplify Square Root of 22704

Here we will show you two methods that you can use to simplify the square root of 22704. In other words, we will show you how to find the square root of 22704 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.

√22704 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 22704 to simplify the square root of 22704. 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 22704. The factors of 22704 are 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 33, 43, 44, 48, 66, 86, 88, 129, 132, 172, 176, 258, 264, 344, 473, 516, 528, 688, 946, 1032, 1419, 1892, 2064, 2838, 3784, 5676, 7568, 11352, and 22704. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 22704 divided by the greatest perfect square from the list of all factors of 22704. We determined above that the greatest perfect square from the list of all factors of 22704 is 16. Furthermore, 22704 divided by 16 is 1419, therefore B equals 1419.

Now we have A and B and can get our answer to 22704 in its simplest radical form as follows:

√22704 = A√B

√22704 = 4√1419

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 22704 to simplify the square root of 22704 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 22704 and then take the square root of that product. The prime factors that multiply together to make 22704 are 2 x 2 x 2 x 2 x 3 x 11 x 43. When we strip out the pairs only, we get 2 x 2 x 2 x 2 = 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Divide 22704 by the number (A) squared. 4 squared is 16 and 22704 divided by 16 is 1419. Therefore, B equals 1419.

Once again we have A and B and can get our answer to 22704 in its simplest radical form as follows:

√22704 = A√B

√22704 = 4√1419

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