Simplify Square Root of 31200

Here we will show you two methods that you can use to simplify the square root of 31200. In other words, we will show you how to find the square root of 31200 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.

√31200 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 31200 to simplify the square root of 31200. 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 31200. The factors of 31200 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 16, 20, 24, 25, 26, 30, 32, 39, 40, 48, 50, 52, 60, 65, 75, 78, 80, 96, 100, 104, 120, 130, 150, 156, 160, 195, 200, 208, 240, 260, 300, 312, 325, 390, 400, 416, 480, 520, 600, 624, 650, 780, 800, 975, 1040, 1200, 1248, 1300, 1560, 1950, 2080, 2400, 2600, 3120, 3900, 5200, 6240, 7800, 10400, 15600, and 31200. Furthermore, the greatest perfect square on this list is 400 and the square root of 400 is 20. Therefore, A equals 20.

B = Calculate 31200 divided by the greatest perfect square from the list of all factors of 31200. We determined above that the greatest perfect square from the list of all factors of 31200 is 400. Furthermore, 31200 divided by 400 is 78, therefore B equals 78.

Now we have A and B and can get our answer to 31200 in its simplest radical form as follows:

√31200 = A√B

√31200 = 20√78

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 31200 to simplify the square root of 31200 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 31200 and then take the square root of that product. The prime factors that multiply together to make 31200 are 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5 x 13. 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 31200 by the number (A) squared. 20 squared is 400 and 31200 divided by 400 is 78. Therefore, B equals 78.

Once again we have A and B and can get our answer to 31200 in its simplest radical form as follows:

√31200 = A√B

√31200 = 20√78

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Simplify Square Root of 31201
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