Simplify Square Root of 36800

Here we will show you two methods that you can use to simplify the square root of 36800. In other words, we will show you how to find the square root of 36800 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.

√36800 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 36800 to simplify the square root of 36800. 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 36800. The factors of 36800 are 1, 2, 4, 5, 8, 10, 16, 20, 23, 25, 32, 40, 46, 50, 64, 80, 92, 100, 115, 160, 184, 200, 230, 320, 368, 400, 460, 575, 736, 800, 920, 1150, 1472, 1600, 1840, 2300, 3680, 4600, 7360, 9200, 18400, and 36800. Furthermore, the greatest perfect square on this list is 1600 and the square root of 1600 is 40. Therefore, A equals 40.

B = Calculate 36800 divided by the greatest perfect square from the list of all factors of 36800. We determined above that the greatest perfect square from the list of all factors of 36800 is 1600. Furthermore, 36800 divided by 1600 is 23, therefore B equals 23.

Now we have A and B and can get our answer to 36800 in its simplest radical form as follows:

√36800 = A√B

√36800 = 40√23

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 36800 to simplify the square root of 36800 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 36800 and then take the square root of that product. The prime factors that multiply together to make 36800 are 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 x 23. 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 36800 by the number (A) squared. 40 squared is 1600 and 36800 divided by 1600 is 23. Therefore, B equals 23.

Once again we have A and B and can get our answer to 36800 in its simplest radical form as follows:

√36800 = A√B

√36800 = 40√23

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