Simplify Square Root of 29376

Here we will show you two methods that you can use to simplify the square root of 29376. In other words, we will show you how to find the square root of 29376 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.

√29376 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 29376 to simplify the square root of 29376. 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 29376. The factors of 29376 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 17, 18, 24, 27, 32, 34, 36, 48, 51, 54, 64, 68, 72, 96, 102, 108, 136, 144, 153, 192, 204, 216, 272, 288, 306, 408, 432, 459, 544, 576, 612, 816, 864, 918, 1088, 1224, 1632, 1728, 1836, 2448, 3264, 3672, 4896, 7344, 9792, 14688, and 29376. Furthermore, the greatest perfect square on this list is 576 and the square root of 576 is 24. Therefore, A equals 24.

B = Calculate 29376 divided by the greatest perfect square from the list of all factors of 29376. We determined above that the greatest perfect square from the list of all factors of 29376 is 576. Furthermore, 29376 divided by 576 is 51, therefore B equals 51.

Now we have A and B and can get our answer to 29376 in its simplest radical form as follows:

√29376 = A√B

√29376 = 24√51

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 29376 to simplify the square root of 29376 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 29376 and then take the square root of that product. The prime factors that multiply together to make 29376 are 2 x 2 x 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 2 x 2 x 3 x 3 = 576 and the square root of 576 is 24. Therefore, A equals 24.

B = Divide 29376 by the number (A) squared. 24 squared is 576 and 29376 divided by 576 is 51. Therefore, B equals 51.

Once again we have A and B and can get our answer to 29376 in its simplest radical form as follows:

√29376 = A√B

√29376 = 24√51

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