Simplify Square Root of 9324

Here we will show you two methods that you can use to simplify the square root of 9324. In other words, we will show you how to find the square root of 9324 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.

√9324 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 9324 to simplify the square root of 9324. 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 9324. The factors of 9324 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 37, 42, 63, 74, 84, 111, 126, 148, 222, 252, 259, 333, 444, 518, 666, 777, 1036, 1332, 1554, 2331, 3108, 4662, and 9324. Furthermore, the greatest perfect square on this list is 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Calculate 9324 divided by the greatest perfect square from the list of all factors of 9324. We determined above that the greatest perfect square from the list of all factors of 9324 is 36. Furthermore, 9324 divided by 36 is 259, therefore B equals 259.

Now we have A and B and can get our answer to 9324 in its simplest radical form as follows:

√9324 = A√B

√9324 = 6√259

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 9324 to simplify the square root of 9324 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 9324 and then take the square root of that product. The prime factors that multiply together to make 9324 are 2 x 2 x 3 x 3 x 7 x 37. 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 9324 by the number (A) squared. 6 squared is 36 and 9324 divided by 36 is 259. Therefore, B equals 259.

Once again we have A and B and can get our answer to 9324 in its simplest radical form as follows:

√9324 = A√B

√9324 = 6√259

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