Simplify Square Root of 93296

Here we will show you two methods that you can use to simplify the square root of 93296. In other words, we will show you how to find the square root of 93296 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.

√93296 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 93296 to simplify the square root of 93296. 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 93296. The factors of 93296 are 1, 2, 4, 7, 8, 14, 16, 17, 28, 34, 49, 56, 68, 98, 112, 119, 136, 196, 238, 272, 343, 392, 476, 686, 784, 833, 952, 1372, 1666, 1904, 2744, 3332, 5488, 5831, 6664, 11662, 13328, 23324, 46648, and 93296. Furthermore, the greatest perfect square on this list is 784 and the square root of 784 is 28. Therefore, A equals 28.

B = Calculate 93296 divided by the greatest perfect square from the list of all factors of 93296. We determined above that the greatest perfect square from the list of all factors of 93296 is 784. Furthermore, 93296 divided by 784 is 119, therefore B equals 119.

Now we have A and B and can get our answer to 93296 in its simplest radical form as follows:

√93296 = A√B

√93296 = 28√119

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 93296 to simplify the square root of 93296 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 93296 and then take the square root of that product. The prime factors that multiply together to make 93296 are 2 x 2 x 2 x 2 x 7 x 7 x 7 x 17. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 7 x 7 = 784 and the square root of 784 is 28. Therefore, A equals 28.

B = Divide 93296 by the number (A) squared. 28 squared is 784 and 93296 divided by 784 is 119. Therefore, B equals 119.

Once again we have A and B and can get our answer to 93296 in its simplest radical form as follows:

√93296 = A√B

√93296 = 28√119

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