Simplify Square Root of 82704

Here we will show you two methods that you can use to simplify the square root of 82704. In other words, we will show you how to find the square root of 82704 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.

√82704 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 82704 to simplify the square root of 82704. 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 82704. The factors of 82704 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1723, 3446, 5169, 6892, 10338, 13784, 20676, 27568, 41352, and 82704. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 82704 divided by the greatest perfect square from the list of all factors of 82704. We determined above that the greatest perfect square from the list of all factors of 82704 is 16. Furthermore, 82704 divided by 16 is 5169, therefore B equals 5169.

Now we have A and B and can get our answer to 82704 in its simplest radical form as follows:

√82704 = A√B

√82704 = 4√5169

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 82704 to simplify the square root of 82704 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 82704 and then take the square root of that product. The prime factors that multiply together to make 82704 are 2 x 2 x 2 x 2 x 3 x 1723. 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 82704 by the number (A) squared. 4 squared is 16 and 82704 divided by 16 is 5169. Therefore, B equals 5169.

Once again we have A and B and can get our answer to 82704 in its simplest radical form as follows:

√82704 = A√B

√82704 = 4√5169

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