Simplify Square Root of 97804

Here we will show you two methods that you can use to simplify the square root of 97804. In other words, we will show you how to find the square root of 97804 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.

√97804 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 97804 to simplify the square root of 97804. 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 97804. The factors of 97804 are 1, 2, 4, 7, 14, 28, 49, 98, 196, 499, 998, 1996, 3493, 6986, 13972, 24451, 48902, and 97804. Furthermore, the greatest perfect square on this list is 196 and the square root of 196 is 14. Therefore, A equals 14.

B = Calculate 97804 divided by the greatest perfect square from the list of all factors of 97804. We determined above that the greatest perfect square from the list of all factors of 97804 is 196. Furthermore, 97804 divided by 196 is 499, therefore B equals 499.

Now we have A and B and can get our answer to 97804 in its simplest radical form as follows:

√97804 = A√B

√97804 = 14√499

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 97804 to simplify the square root of 97804 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 97804 and then take the square root of that product. The prime factors that multiply together to make 97804 are 2 x 2 x 7 x 7 x 499. When we strip out the pairs only, we get 2 x 2 x 7 x 7 = 196 and the square root of 196 is 14. Therefore, A equals 14.

B = Divide 97804 by the number (A) squared. 14 squared is 196 and 97804 divided by 196 is 499. Therefore, B equals 499.

Once again we have A and B and can get our answer to 97804 in its simplest radical form as follows:

√97804 = A√B

√97804 = 14√499

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Simplify Square Root of 97805
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