Simplify Square Root of 97225

Here we will show you two methods that you can use to simplify the square root of 97225. In other words, we will show you how to find the square root of 97225 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.

√97225 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 97225 to simplify the square root of 97225. 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 97225. The factors of 97225 are 1, 5, 25, 3889, 19445, and 97225. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 97225 divided by the greatest perfect square from the list of all factors of 97225. We determined above that the greatest perfect square from the list of all factors of 97225 is 25. Furthermore, 97225 divided by 25 is 3889, therefore B equals 3889.

Now we have A and B and can get our answer to 97225 in its simplest radical form as follows:

√97225 = A√B

√97225 = 5√3889

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 97225 to simplify the square root of 97225 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 97225 and then take the square root of that product. The prime factors that multiply together to make 97225 are 5 x 5 x 3889. When we strip out the pairs only, we get 5 x 5 = 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Divide 97225 by the number (A) squared. 5 squared is 25 and 97225 divided by 25 is 3889. Therefore, B equals 3889.

Once again we have A and B and can get our answer to 97225 in its simplest radical form as follows:

√97225 = A√B

√97225 = 5√3889

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