Simplify Square Root of 93104

Here we will show you two methods that you can use to simplify the square root of 93104. In other words, we will show you how to find the square root of 93104 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.

√93104 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 93104 to simplify the square root of 93104. 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 93104. The factors of 93104 are 1, 2, 4, 8, 11, 16, 22, 23, 44, 46, 88, 92, 176, 184, 253, 368, 506, 529, 1012, 1058, 2024, 2116, 4048, 4232, 5819, 8464, 11638, 23276, 46552, and 93104. Furthermore, the greatest perfect square on this list is 8464 and the square root of 8464 is 92. Therefore, A equals 92.

B = Calculate 93104 divided by the greatest perfect square from the list of all factors of 93104. We determined above that the greatest perfect square from the list of all factors of 93104 is 8464. Furthermore, 93104 divided by 8464 is 11, therefore B equals 11.

Now we have A and B and can get our answer to 93104 in its simplest radical form as follows:

√93104 = A√B

√93104 = 92√11

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 93104 to simplify the square root of 93104 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 93104 and then take the square root of that product. The prime factors that multiply together to make 93104 are 2 x 2 x 2 x 2 x 11 x 23 x 23. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 23 x 23 = 8464 and the square root of 8464 is 92. Therefore, A equals 92.

B = Divide 93104 by the number (A) squared. 92 squared is 8464 and 93104 divided by 8464 is 11. Therefore, B equals 11.

Once again we have A and B and can get our answer to 93104 in its simplest radical form as follows:

√93104 = A√B

√93104 = 92√11

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