Simplify Square Root of 66792

Here we will show you two methods that you can use to simplify the square root of 66792. In other words, we will show you how to find the square root of 66792 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.

√66792 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 66792 to simplify the square root of 66792. 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 66792. The factors of 66792 are 1, 2, 3, 4, 6, 8, 11, 12, 22, 23, 24, 33, 44, 46, 66, 69, 88, 92, 121, 132, 138, 184, 242, 253, 264, 276, 363, 484, 506, 552, 726, 759, 968, 1012, 1452, 1518, 2024, 2783, 2904, 3036, 5566, 6072, 8349, 11132, 16698, 22264, 33396, and 66792. Furthermore, the greatest perfect square on this list is 484 and the square root of 484 is 22. Therefore, A equals 22.

B = Calculate 66792 divided by the greatest perfect square from the list of all factors of 66792. We determined above that the greatest perfect square from the list of all factors of 66792 is 484. Furthermore, 66792 divided by 484 is 138, therefore B equals 138.

Now we have A and B and can get our answer to 66792 in its simplest radical form as follows:

√66792 = A√B

√66792 = 22√138

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 66792 to simplify the square root of 66792 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 66792 and then take the square root of that product. The prime factors that multiply together to make 66792 are 2 x 2 x 2 x 3 x 11 x 11 x 23. When we strip out the pairs only, we get 2 x 2 x 11 x 11 = 484 and the square root of 484 is 22. Therefore, A equals 22.

B = Divide 66792 by the number (A) squared. 22 squared is 484 and 66792 divided by 484 is 138. Therefore, B equals 138.

Once again we have A and B and can get our answer to 66792 in its simplest radical form as follows:

√66792 = A√B

√66792 = 22√138

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