Simplify Square Root of 97092

Here we will show you two methods that you can use to simplify the square root of 97092. In other words, we will show you how to find the square root of 97092 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.

√97092 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 97092 to simplify the square root of 97092. 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 97092. The factors of 97092 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 29, 31, 36, 54, 58, 62, 87, 93, 108, 116, 124, 174, 186, 261, 279, 348, 372, 522, 558, 783, 837, 899, 1044, 1116, 1566, 1674, 1798, 2697, 3132, 3348, 3596, 5394, 8091, 10788, 16182, 24273, 32364, 48546, and 97092. Furthermore, the greatest perfect square on this list is 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Calculate 97092 divided by the greatest perfect square from the list of all factors of 97092. We determined above that the greatest perfect square from the list of all factors of 97092 is 36. Furthermore, 97092 divided by 36 is 2697, therefore B equals 2697.

Now we have A and B and can get our answer to 97092 in its simplest radical form as follows:

√97092 = A√B

√97092 = 6√2697

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 97092 to simplify the square root of 97092 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 97092 and then take the square root of that product. The prime factors that multiply together to make 97092 are 2 x 2 x 3 x 3 x 3 x 29 x 31. When we strip out the pairs only, we get 2 x 2 x 3 x 3 = 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Divide 97092 by the number (A) squared. 6 squared is 36 and 97092 divided by 36 is 2697. Therefore, B equals 2697.

Once again we have A and B and can get our answer to 97092 in its simplest radical form as follows:

√97092 = A√B

√97092 = 6√2697

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