Simplify Square Root of 83148

Here we will show you two methods that you can use to simplify the square root of 83148. In other words, we will show you how to find the square root of 83148 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.

√83148 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 83148 to simplify the square root of 83148. 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 83148. The factors of 83148 are 1, 2, 3, 4, 6, 12, 13, 26, 39, 41, 52, 78, 82, 123, 156, 164, 169, 246, 338, 492, 507, 533, 676, 1014, 1066, 1599, 2028, 2132, 3198, 6396, 6929, 13858, 20787, 27716, 41574, and 83148. Furthermore, the greatest perfect square on this list is 676 and the square root of 676 is 26. Therefore, A equals 26.

B = Calculate 83148 divided by the greatest perfect square from the list of all factors of 83148. We determined above that the greatest perfect square from the list of all factors of 83148 is 676. Furthermore, 83148 divided by 676 is 123, therefore B equals 123.

Now we have A and B and can get our answer to 83148 in its simplest radical form as follows:

√83148 = A√B

√83148 = 26√123

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 83148 to simplify the square root of 83148 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 83148 and then take the square root of that product. The prime factors that multiply together to make 83148 are 2 x 2 x 3 x 13 x 13 x 41. When we strip out the pairs only, we get 2 x 2 x 13 x 13 = 676 and the square root of 676 is 26. Therefore, A equals 26.

B = Divide 83148 by the number (A) squared. 26 squared is 676 and 83148 divided by 676 is 123. Therefore, B equals 123.

Once again we have A and B and can get our answer to 83148 in its simplest radical form as follows:

√83148 = A√B

√83148 = 26√123

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