Simplify Square Root of 97902

Here we will show you two methods that you can use to simplify the square root of 97902. In other words, we will show you how to find the square root of 97902 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.

√97902 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 97902 to simplify the square root of 97902. 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 97902. The factors of 97902 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 37, 42, 49, 54, 63, 74, 98, 111, 126, 147, 189, 222, 259, 294, 333, 378, 441, 518, 666, 777, 882, 999, 1323, 1554, 1813, 1998, 2331, 2646, 3626, 4662, 5439, 6993, 10878, 13986, 16317, 32634, 48951, and 97902. Furthermore, the greatest perfect square on this list is 441 and the square root of 441 is 21. Therefore, A equals 21.

B = Calculate 97902 divided by the greatest perfect square from the list of all factors of 97902. We determined above that the greatest perfect square from the list of all factors of 97902 is 441. Furthermore, 97902 divided by 441 is 222, therefore B equals 222.

Now we have A and B and can get our answer to 97902 in its simplest radical form as follows:

√97902 = A√B

√97902 = 21√222

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 97902 to simplify the square root of 97902 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 97902 and then take the square root of that product. The prime factors that multiply together to make 97902 are 2 x 3 x 3 x 3 x 7 x 7 x 37. When we strip out the pairs only, we get 3 x 3 x 7 x 7 = 441 and the square root of 441 is 21. Therefore, A equals 21.

B = Divide 97902 by the number (A) squared. 21 squared is 441 and 97902 divided by 441 is 222. Therefore, B equals 222.

Once again we have A and B and can get our answer to 97902 in its simplest radical form as follows:

√97902 = A√B

√97902 = 21√222

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