Simplify Square Root of 97498

Here we will show you two methods that you can use to simplify the square root of 97498. In other words, we will show you how to find the square root of 97498 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.

√97498 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 97498 to simplify the square root of 97498. 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 97498. The factors of 97498 are 1, 2, 29, 41, 58, 82, 1189, 1681, 2378, 3362, 48749, and 97498. Furthermore, the greatest perfect square on this list is 1681 and the square root of 1681 is 41. Therefore, A equals 41.

B = Calculate 97498 divided by the greatest perfect square from the list of all factors of 97498. We determined above that the greatest perfect square from the list of all factors of 97498 is 1681. Furthermore, 97498 divided by 1681 is 58, therefore B equals 58.

Now we have A and B and can get our answer to 97498 in its simplest radical form as follows:

√97498 = A√B

√97498 = 41√58

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 97498 to simplify the square root of 97498 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 97498 and then take the square root of that product. The prime factors that multiply together to make 97498 are 2 x 29 x 41 x 41. When we strip out the pairs only, we get 41 x 41 = 1681 and the square root of 1681 is 41. Therefore, A equals 41.

B = Divide 97498 by the number (A) squared. 41 squared is 1681 and 97498 divided by 1681 is 58. Therefore, B equals 58.

Once again we have A and B and can get our answer to 97498 in its simplest radical form as follows:

√97498 = A√B

√97498 = 41√58

Simplify Square Root
Please enter another square root in the box below for us to simplify.

Simplify Square Root of 97499
Here is the next square root on our list that we have simplifed for you.