Simplify Square Root of 30192

Here we will show you two methods that you can use to simplify the square root of 30192. In other words, we will show you how to find the square root of 30192 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.

√30192 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 30192 to simplify the square root of 30192. 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 30192. The factors of 30192 are 1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 34, 37, 48, 51, 68, 74, 102, 111, 136, 148, 204, 222, 272, 296, 408, 444, 592, 629, 816, 888, 1258, 1776, 1887, 2516, 3774, 5032, 7548, 10064, 15096, and 30192. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 30192 divided by the greatest perfect square from the list of all factors of 30192. We determined above that the greatest perfect square from the list of all factors of 30192 is 16. Furthermore, 30192 divided by 16 is 1887, therefore B equals 1887.

Now we have A and B and can get our answer to 30192 in its simplest radical form as follows:

√30192 = A√B

√30192 = 4√1887

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 30192 to simplify the square root of 30192 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 30192 and then take the square root of that product. The prime factors that multiply together to make 30192 are 2 x 2 x 2 x 2 x 3 x 17 x 37. 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 30192 by the number (A) squared. 4 squared is 16 and 30192 divided by 16 is 1887. Therefore, B equals 1887.

Once again we have A and B and can get our answer to 30192 in its simplest radical form as follows:

√30192 = A√B

√30192 = 4√1887

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