Simplify Square Root of 83032

Here we will show you two methods that you can use to simplify the square root of 83032. In other words, we will show you how to find the square root of 83032 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.

√83032 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 83032 to simplify the square root of 83032. 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 83032. The factors of 83032 are 1, 2, 4, 8, 97, 107, 194, 214, 388, 428, 776, 856, 10379, 20758, 41516, and 83032. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 83032 divided by the greatest perfect square from the list of all factors of 83032. We determined above that the greatest perfect square from the list of all factors of 83032 is 4. Furthermore, 83032 divided by 4 is 20758, therefore B equals 20758.

Now we have A and B and can get our answer to 83032 in its simplest radical form as follows:

√83032 = A√B

√83032 = 2√20758

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 83032 to simplify the square root of 83032 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 83032 and then take the square root of that product. The prime factors that multiply together to make 83032 are 2 x 2 x 2 x 97 x 107. When we strip out the pairs only, we get 2 x 2 = 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Divide 83032 by the number (A) squared. 2 squared is 4 and 83032 divided by 4 is 20758. Therefore, B equals 20758.

Once again we have A and B and can get our answer to 83032 in its simplest radical form as follows:

√83032 = A√B

√83032 = 2√20758

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Simplify Square Root of 83033
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