Simplify Square Root of 16317

Here we will show you two methods that you can use to simplify the square root of 16317. In other words, we will show you how to find the square root of 16317 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.

√16317 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 16317 to simplify the square root of 16317. 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 16317. The factors of 16317 are 1, 3, 7, 9, 21, 37, 49, 63, 111, 147, 259, 333, 441, 777, 1813, 2331, 5439, and 16317. Furthermore, the greatest perfect square on this list is 441 and the square root of 441 is 21. Therefore, A equals 21.

B = Calculate 16317 divided by the greatest perfect square from the list of all factors of 16317. We determined above that the greatest perfect square from the list of all factors of 16317 is 441. Furthermore, 16317 divided by 441 is 37, therefore B equals 37.

Now we have A and B and can get our answer to 16317 in its simplest radical form as follows:

√16317 = A√B

√16317 = 21√37

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 16317 to simplify the square root of 16317 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 16317 and then take the square root of that product. The prime factors that multiply together to make 16317 are 3 x 3 x 7 x 7 x 37. When we strip out the pairs only, we get 3 x 3 x 7 x 7 = 441 and the square root of 441 is 21. Therefore, A equals 21.

B = Divide 16317 by the number (A) squared. 21 squared is 441 and 16317 divided by 441 is 37. Therefore, B equals 37.

Once again we have A and B and can get our answer to 16317 in its simplest radical form as follows:

√16317 = A√B

√16317 = 21√37

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Simplify Square Root of 16318
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