Simplify Square Root of 30324

Here we will show you two methods that you can use to simplify the square root of 30324. In other words, we will show you how to find the square root of 30324 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.

√30324 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 30324 to simplify the square root of 30324. 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 30324. The factors of 30324 are 1, 2, 3, 4, 6, 7, 12, 14, 19, 21, 28, 38, 42, 57, 76, 84, 114, 133, 228, 266, 361, 399, 532, 722, 798, 1083, 1444, 1596, 2166, 2527, 4332, 5054, 7581, 10108, 15162, and 30324. Furthermore, the greatest perfect square on this list is 1444 and the square root of 1444 is 38. Therefore, A equals 38.

B = Calculate 30324 divided by the greatest perfect square from the list of all factors of 30324. We determined above that the greatest perfect square from the list of all factors of 30324 is 1444. Furthermore, 30324 divided by 1444 is 21, therefore B equals 21.

Now we have A and B and can get our answer to 30324 in its simplest radical form as follows:

√30324 = A√B

√30324 = 38√21

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 30324 to simplify the square root of 30324 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 30324 and then take the square root of that product. The prime factors that multiply together to make 30324 are 2 x 2 x 3 x 7 x 19 x 19. When we strip out the pairs only, we get 2 x 2 x 19 x 19 = 1444 and the square root of 1444 is 38. Therefore, A equals 38.

B = Divide 30324 by the number (A) squared. 38 squared is 1444 and 30324 divided by 1444 is 21. Therefore, B equals 21.

Once again we have A and B and can get our answer to 30324 in its simplest radical form as follows:

√30324 = A√B

√30324 = 38√21

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