Simplify Square Root of 83006

Here we will show you two methods that you can use to simplify the square root of 83006. In other words, we will show you how to find the square root of 83006 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.

√83006 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 83006 to simplify the square root of 83006. 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 83006. The factors of 83006 are 1, 2, 7, 11, 14, 22, 49, 77, 98, 121, 154, 242, 343, 539, 686, 847, 1078, 1694, 3773, 5929, 7546, 11858, 41503, and 83006. Furthermore, the greatest perfect square on this list is 5929 and the square root of 5929 is 77. Therefore, A equals 77.

B = Calculate 83006 divided by the greatest perfect square from the list of all factors of 83006. We determined above that the greatest perfect square from the list of all factors of 83006 is 5929. Furthermore, 83006 divided by 5929 is 14, therefore B equals 14.

Now we have A and B and can get our answer to 83006 in its simplest radical form as follows:

√83006 = A√B

√83006 = 77√14

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 83006 to simplify the square root of 83006 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 83006 and then take the square root of that product. The prime factors that multiply together to make 83006 are 2 x 7 x 7 x 7 x 11 x 11. When we strip out the pairs only, we get 7 x 7 x 11 x 11 = 5929 and the square root of 5929 is 77. Therefore, A equals 77.

B = Divide 83006 by the number (A) squared. 77 squared is 5929 and 83006 divided by 5929 is 14. Therefore, B equals 14.

Once again we have A and B and can get our answer to 83006 in its simplest radical form as follows:

√83006 = A√B

√83006 = 77√14

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