Simplify Square Root of 83800

Here we will show you two methods that you can use to simplify the square root of 83800. In other words, we will show you how to find the square root of 83800 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.

√83800 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 83800 to simplify the square root of 83800. 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 83800. The factors of 83800 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200, 419, 838, 1676, 2095, 3352, 4190, 8380, 10475, 16760, 20950, 41900, and 83800. Furthermore, the greatest perfect square on this list is 100 and the square root of 100 is 10. Therefore, A equals 10.

B = Calculate 83800 divided by the greatest perfect square from the list of all factors of 83800. We determined above that the greatest perfect square from the list of all factors of 83800 is 100. Furthermore, 83800 divided by 100 is 838, therefore B equals 838.

Now we have A and B and can get our answer to 83800 in its simplest radical form as follows:

√83800 = A√B

√83800 = 10√838

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 83800 to simplify the square root of 83800 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 83800 and then take the square root of that product. The prime factors that multiply together to make 83800 are 2 x 2 x 2 x 5 x 5 x 419. When we strip out the pairs only, we get 2 x 2 x 5 x 5 = 100 and the square root of 100 is 10. Therefore, A equals 10.

B = Divide 83800 by the number (A) squared. 10 squared is 100 and 83800 divided by 100 is 838. Therefore, B equals 838.

Once again we have A and B and can get our answer to 83800 in its simplest radical form as follows:

√83800 = A√B

√83800 = 10√838

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