Simplify Square Root of 72324

Here we will show you two methods that you can use to simplify the square root of 72324. In other words, we will show you how to find the square root of 72324 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.

√72324 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 72324 to simplify the square root of 72324. 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 72324. The factors of 72324 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 41, 42, 49, 63, 82, 84, 98, 123, 126, 147, 164, 196, 246, 252, 287, 294, 369, 441, 492, 574, 588, 738, 861, 882, 1148, 1476, 1722, 1764, 2009, 2583, 3444, 4018, 5166, 6027, 8036, 10332, 12054, 18081, 24108, 36162, and 72324. Furthermore, the greatest perfect square on this list is 1764 and the square root of 1764 is 42. Therefore, A equals 42.

B = Calculate 72324 divided by the greatest perfect square from the list of all factors of 72324. We determined above that the greatest perfect square from the list of all factors of 72324 is 1764. Furthermore, 72324 divided by 1764 is 41, therefore B equals 41.

Now we have A and B and can get our answer to 72324 in its simplest radical form as follows:

√72324 = A√B

√72324 = 42√41

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 72324 to simplify the square root of 72324 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 72324 and then take the square root of that product. The prime factors that multiply together to make 72324 are 2 x 2 x 3 x 3 x 7 x 7 x 41. When we strip out the pairs only, we get 2 x 2 x 3 x 3 x 7 x 7 = 1764 and the square root of 1764 is 42. Therefore, A equals 42.

B = Divide 72324 by the number (A) squared. 42 squared is 1764 and 72324 divided by 1764 is 41. Therefore, B equals 41.

Once again we have A and B and can get our answer to 72324 in its simplest radical form as follows:

√72324 = A√B

√72324 = 42√41

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