Simplify Square Root of 74368

Here we will show you two methods that you can use to simplify the square root of 74368. In other words, we will show you how to find the square root of 74368 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.

√74368 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 74368 to simplify the square root of 74368. 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 74368. The factors of 74368 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 83, 112, 128, 166, 224, 332, 448, 581, 664, 896, 1162, 1328, 2324, 2656, 4648, 5312, 9296, 10624, 18592, 37184, and 74368. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 74368 divided by the greatest perfect square from the list of all factors of 74368. We determined above that the greatest perfect square from the list of all factors of 74368 is 64. Furthermore, 74368 divided by 64 is 1162, therefore B equals 1162.

Now we have A and B and can get our answer to 74368 in its simplest radical form as follows:

√74368 = A√B

√74368 = 8√1162

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 74368 to simplify the square root of 74368 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 74368 and then take the square root of that product. The prime factors that multiply together to make 74368 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 7 x 83. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 = 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Divide 74368 by the number (A) squared. 8 squared is 64 and 74368 divided by 64 is 1162. Therefore, B equals 1162.

Once again we have A and B and can get our answer to 74368 in its simplest radical form as follows:

√74368 = A√B

√74368 = 8√1162

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