Simplify Square Root of 96800

Here we will show you two methods that you can use to simplify the square root of 96800. In other words, we will show you how to find the square root of 96800 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.

√96800 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 96800 to simplify the square root of 96800. 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 96800. The factors of 96800 are 1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 25, 32, 40, 44, 50, 55, 80, 88, 100, 110, 121, 160, 176, 200, 220, 242, 275, 352, 400, 440, 484, 550, 605, 800, 880, 968, 1100, 1210, 1760, 1936, 2200, 2420, 3025, 3872, 4400, 4840, 6050, 8800, 9680, 12100, 19360, 24200, 48400, and 96800. Furthermore, the greatest perfect square on this list is 48400 and the square root of 48400 is 220. Therefore, A equals 220.

B = Calculate 96800 divided by the greatest perfect square from the list of all factors of 96800. We determined above that the greatest perfect square from the list of all factors of 96800 is 48400. Furthermore, 96800 divided by 48400 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 96800 in its simplest radical form as follows:

√96800 = A√B

√96800 = 220√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 96800 to simplify the square root of 96800 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 96800 and then take the square root of that product. The prime factors that multiply together to make 96800 are 2 x 2 x 2 x 2 x 2 x 5 x 5 x 11 x 11. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 5 x 5 x 11 x 11 = 48400 and the square root of 48400 is 220. Therefore, A equals 220.

B = Divide 96800 by the number (A) squared. 220 squared is 48400 and 96800 divided by 48400 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 96800 in its simplest radical form as follows:

√96800 = A√B

√96800 = 220√2

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