Simplify Square Root of 97199

Here we will show you two methods that you can use to simplify the square root of 97199. In other words, we will show you how to find the square root of 97199 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.

√97199 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 97199 to simplify the square root of 97199. 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 97199. The factors of 97199 are 1, 37, 71, 1369, 2627, and 97199. Furthermore, the greatest perfect square on this list is 1369 and the square root of 1369 is 37. Therefore, A equals 37.

B = Calculate 97199 divided by the greatest perfect square from the list of all factors of 97199. We determined above that the greatest perfect square from the list of all factors of 97199 is 1369. Furthermore, 97199 divided by 1369 is 71, therefore B equals 71.

Now we have A and B and can get our answer to 97199 in its simplest radical form as follows:

√97199 = A√B

√97199 = 37√71

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 97199 to simplify the square root of 97199 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 97199 and then take the square root of that product. The prime factors that multiply together to make 97199 are 37 x 37 x 71. When we strip out the pairs only, we get 37 x 37 = 1369 and the square root of 1369 is 37. Therefore, A equals 37.

B = Divide 97199 by the number (A) squared. 37 squared is 1369 and 97199 divided by 1369 is 71. Therefore, B equals 71.

Once again we have A and B and can get our answer to 97199 in its simplest radical form as follows:

√97199 = A√B

√97199 = 37√71

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Simplify Square Root of 97200
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