Simplify Square Root of 97744

Here we will show you two methods that you can use to simplify the square root of 97744. In other words, we will show you how to find the square root of 97744 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.

√97744 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 97744 to simplify the square root of 97744. 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 97744. The factors of 97744 are 1, 2, 4, 8, 16, 41, 82, 149, 164, 298, 328, 596, 656, 1192, 2384, 6109, 12218, 24436, 48872, and 97744. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 97744 divided by the greatest perfect square from the list of all factors of 97744. We determined above that the greatest perfect square from the list of all factors of 97744 is 16. Furthermore, 97744 divided by 16 is 6109, therefore B equals 6109.

Now we have A and B and can get our answer to 97744 in its simplest radical form as follows:

√97744 = A√B

√97744 = 4√6109

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 97744 to simplify the square root of 97744 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 97744 and then take the square root of that product. The prime factors that multiply together to make 97744 are 2 x 2 x 2 x 2 x 41 x 149. When we strip out the pairs only, we get 2 x 2 x 2 x 2 = 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Divide 97744 by the number (A) squared. 4 squared is 16 and 97744 divided by 16 is 6109. Therefore, B equals 6109.

Once again we have A and B and can get our answer to 97744 in its simplest radical form as follows:

√97744 = A√B

√97744 = 4√6109

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