Simplify Square Root of 7344

Here we will show you two methods that you can use to simplify the square root of 7344. In other words, we will show you how to find the square root of 7344 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.

√7344 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 7344 to simplify the square root of 7344. 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 7344. The factors of 7344 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 17, 18, 24, 27, 34, 36, 48, 51, 54, 68, 72, 102, 108, 136, 144, 153, 204, 216, 272, 306, 408, 432, 459, 612, 816, 918, 1224, 1836, 2448, 3672, and 7344. Furthermore, the greatest perfect square on this list is 144 and the square root of 144 is 12. Therefore, A equals 12.

B = Calculate 7344 divided by the greatest perfect square from the list of all factors of 7344. We determined above that the greatest perfect square from the list of all factors of 7344 is 144. Furthermore, 7344 divided by 144 is 51, therefore B equals 51.

Now we have A and B and can get our answer to 7344 in its simplest radical form as follows:

√7344 = A√B

√7344 = 12√51

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 7344 to simplify the square root of 7344 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 7344 and then take the square root of that product. The prime factors that multiply together to make 7344 are 2 x 2 x 2 x 2 x 3 x 3 x 3 x 17. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 3 x 3 = 144 and the square root of 144 is 12. Therefore, A equals 12.

B = Divide 7344 by the number (A) squared. 12 squared is 144 and 7344 divided by 144 is 51. Therefore, B equals 51.

Once again we have A and B and can get our answer to 7344 in its simplest radical form as follows:

√7344 = A√B

√7344 = 12√51

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