Simplify Square Root of 97109

Here we will show you two methods that you can use to simplify the square root of 97109. In other words, we will show you how to find the square root of 97109 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.

√97109 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 97109 to simplify the square root of 97109. 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 97109. The factors of 97109 are 1, 19, 269, 361, 5111, and 97109. Furthermore, the greatest perfect square on this list is 361 and the square root of 361 is 19. Therefore, A equals 19.

B = Calculate 97109 divided by the greatest perfect square from the list of all factors of 97109. We determined above that the greatest perfect square from the list of all factors of 97109 is 361. Furthermore, 97109 divided by 361 is 269, therefore B equals 269.

Now we have A and B and can get our answer to 97109 in its simplest radical form as follows:

√97109 = A√B

√97109 = 19√269

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 97109 to simplify the square root of 97109 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 97109 and then take the square root of that product. The prime factors that multiply together to make 97109 are 19 x 19 x 269. When we strip out the pairs only, we get 19 x 19 = 361 and the square root of 361 is 19. Therefore, A equals 19.

B = Divide 97109 by the number (A) squared. 19 squared is 361 and 97109 divided by 361 is 269. Therefore, B equals 269.

Once again we have A and B and can get our answer to 97109 in its simplest radical form as follows:

√97109 = A√B

√97109 = 19√269

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