Simplify Square Root of 96400

Here we will show you two methods that you can use to simplify the square root of 96400. In other words, we will show you how to find the square root of 96400 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.

√96400 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 96400 to simplify the square root of 96400. 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 96400. The factors of 96400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 241, 400, 482, 964, 1205, 1928, 2410, 3856, 4820, 6025, 9640, 12050, 19280, 24100, 48200, and 96400. Furthermore, the greatest perfect square on this list is 400 and the square root of 400 is 20. Therefore, A equals 20.

B = Calculate 96400 divided by the greatest perfect square from the list of all factors of 96400. We determined above that the greatest perfect square from the list of all factors of 96400 is 400. Furthermore, 96400 divided by 400 is 241, therefore B equals 241.

Now we have A and B and can get our answer to 96400 in its simplest radical form as follows:

√96400 = A√B

√96400 = 20√241

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 96400 to simplify the square root of 96400 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 96400 and then take the square root of that product. The prime factors that multiply together to make 96400 are 2 x 2 x 2 x 2 x 5 x 5 x 241. 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 96400 by the number (A) squared. 20 squared is 400 and 96400 divided by 400 is 241. Therefore, B equals 241.

Once again we have A and B and can get our answer to 96400 in its simplest radical form as follows:

√96400 = A√B

√96400 = 20√241

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