Simplify Square Root of 81600

Here we will show you two methods that you can use to simplify the square root of 81600. In other words, we will show you how to find the square root of 81600 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.

√81600 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 81600 to simplify the square root of 81600. 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 81600. The factors of 81600 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20, 24, 25, 30, 32, 34, 40, 48, 50, 51, 60, 64, 68, 75, 80, 85, 96, 100, 102, 120, 136, 150, 160, 170, 192, 200, 204, 240, 255, 272, 300, 320, 340, 400, 408, 425, 480, 510, 544, 600, 680, 800, 816, 850, 960, 1020, 1088, 1200, 1275, 1360, 1600, 1632, 1700, 2040, 2400, 2550, 2720, 3264, 3400, 4080, 4800, 5100, 5440, 6800, 8160, 10200, 13600, 16320, 20400, 27200, 40800, and 81600. Furthermore, the greatest perfect square on this list is 1600 and the square root of 1600 is 40. Therefore, A equals 40.

B = Calculate 81600 divided by the greatest perfect square from the list of all factors of 81600. We determined above that the greatest perfect square from the list of all factors of 81600 is 1600. Furthermore, 81600 divided by 1600 is 51, therefore B equals 51.

Now we have A and B and can get our answer to 81600 in its simplest radical form as follows:

√81600 = A√B

√81600 = 40√51

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 81600 to simplify the square root of 81600 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 81600 and then take the square root of that product. The prime factors that multiply together to make 81600 are 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5 x 17. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 = 1600 and the square root of 1600 is 40. Therefore, A equals 40.

B = Divide 81600 by the number (A) squared. 40 squared is 1600 and 81600 divided by 1600 is 51. Therefore, B equals 51.

Once again we have A and B and can get our answer to 81600 in its simplest radical form as follows:

√81600 = A√B

√81600 = 40√51

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Simplify Square Root of 81601
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