Simplify Square Root of 86800

Here we will show you two methods that you can use to simplify the square root of 86800. In other words, we will show you how to find the square root of 86800 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.

√86800 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 86800 to simplify the square root of 86800. 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 86800. The factors of 86800 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 31, 35, 40, 50, 56, 62, 70, 80, 100, 112, 124, 140, 155, 175, 200, 217, 248, 280, 310, 350, 400, 434, 496, 560, 620, 700, 775, 868, 1085, 1240, 1400, 1550, 1736, 2170, 2480, 2800, 3100, 3472, 4340, 5425, 6200, 8680, 10850, 12400, 17360, 21700, 43400, and 86800. Furthermore, the greatest perfect square on this list is 400 and the square root of 400 is 20. Therefore, A equals 20.

B = Calculate 86800 divided by the greatest perfect square from the list of all factors of 86800. We determined above that the greatest perfect square from the list of all factors of 86800 is 400. Furthermore, 86800 divided by 400 is 217, therefore B equals 217.

Now we have A and B and can get our answer to 86800 in its simplest radical form as follows:

√86800 = A√B

√86800 = 20√217

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 86800 to simplify the square root of 86800 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 86800 and then take the square root of that product. The prime factors that multiply together to make 86800 are 2 x 2 x 2 x 2 x 5 x 5 x 7 x 31. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 5 x 5 = 400 and the square root of 400 is 20. Therefore, A equals 20.

B = Divide 86800 by the number (A) squared. 20 squared is 400 and 86800 divided by 400 is 217. Therefore, B equals 217.

Once again we have A and B and can get our answer to 86800 in its simplest radical form as follows:

√86800 = A√B

√86800 = 20√217

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