Simplify Square Root of 9200

Here we will show you two methods that you can use to simplify the square root of 9200. In other words, we will show you how to find the square root of 9200 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.

√9200 = A√B

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

B = Calculate 9200 divided by the greatest perfect square from the list of all factors of 9200. We determined above that the greatest perfect square from the list of all factors of 9200 is 400. Furthermore, 9200 divided by 400 is 23, therefore B equals 23.

Now we have A and B and can get our answer to 9200 in its simplest radical form as follows:

√9200 = A√B

√9200 = 20√23

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 9200 to simplify the square root of 9200 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 9200 and then take the square root of that product. The prime factors that multiply together to make 9200 are 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 5 x 5 = 400 and the square root of 400 is 20. Therefore, A equals 20.

B = Divide 9200 by the number (A) squared. 20 squared is 400 and 9200 divided by 400 is 23. Therefore, B equals 23.

Once again we have A and B and can get our answer to 9200 in its simplest radical form as follows:

√9200 = A√B

√9200 = 20√23

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Simplify Square Root of 9201
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