Simplify Square Root of 79584

Here we will show you two methods that you can use to simplify the square root of 79584. In other words, we will show you how to find the square root of 79584 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.

√79584 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 79584 to simplify the square root of 79584. 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 79584. The factors of 79584 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 829, 1658, 2487, 3316, 4974, 6632, 9948, 13264, 19896, 26528, 39792, and 79584. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 79584 divided by the greatest perfect square from the list of all factors of 79584. We determined above that the greatest perfect square from the list of all factors of 79584 is 16. Furthermore, 79584 divided by 16 is 4974, therefore B equals 4974.

Now we have A and B and can get our answer to 79584 in its simplest radical form as follows:

√79584 = A√B

√79584 = 4√4974

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 79584 to simplify the square root of 79584 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 79584 and then take the square root of that product. The prime factors that multiply together to make 79584 are 2 x 2 x 2 x 2 x 2 x 3 x 829. When we strip out the pairs only, we get 2 x 2 x 2 x 2 = 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Divide 79584 by the number (A) squared. 4 squared is 16 and 79584 divided by 16 is 4974. Therefore, B equals 4974.

Once again we have A and B and can get our answer to 79584 in its simplest radical form as follows:

√79584 = A√B

√79584 = 4√4974

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