Simplify Square Root of 84192

Here we will show you two methods that you can use to simplify the square root of 84192. In other words, we will show you how to find the square root of 84192 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.

√84192 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 84192 to simplify the square root of 84192. 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 84192. The factors of 84192 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 877, 1754, 2631, 3508, 5262, 7016, 10524, 14032, 21048, 28064, 42096, and 84192. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 84192 divided by the greatest perfect square from the list of all factors of 84192. We determined above that the greatest perfect square from the list of all factors of 84192 is 16. Furthermore, 84192 divided by 16 is 5262, therefore B equals 5262.

Now we have A and B and can get our answer to 84192 in its simplest radical form as follows:

√84192 = A√B

√84192 = 4√5262

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 84192 to simplify the square root of 84192 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 84192 and then take the square root of that product. The prime factors that multiply together to make 84192 are 2 x 2 x 2 x 2 x 2 x 3 x 877. 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 84192 by the number (A) squared. 4 squared is 16 and 84192 divided by 16 is 5262. Therefore, B equals 5262.

Once again we have A and B and can get our answer to 84192 in its simplest radical form as follows:

√84192 = A√B

√84192 = 4√5262

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Simplify Square Root of 84193
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