Simplify Square Root of 92064

Here we will show you two methods that you can use to simplify the square root of 92064. In other words, we will show you how to find the square root of 92064 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.

√92064 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 92064 to simplify the square root of 92064. 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 92064. The factors of 92064 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 112, 137, 168, 224, 274, 336, 411, 548, 672, 822, 959, 1096, 1644, 1918, 2192, 2877, 3288, 3836, 4384, 5754, 6576, 7672, 11508, 13152, 15344, 23016, 30688, 46032, and 92064. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 92064 divided by the greatest perfect square from the list of all factors of 92064. We determined above that the greatest perfect square from the list of all factors of 92064 is 16. Furthermore, 92064 divided by 16 is 5754, therefore B equals 5754.

Now we have A and B and can get our answer to 92064 in its simplest radical form as follows:

√92064 = A√B

√92064 = 4√5754

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 92064 to simplify the square root of 92064 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 92064 and then take the square root of that product. The prime factors that multiply together to make 92064 are 2 x 2 x 2 x 2 x 2 x 3 x 7 x 137. 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 92064 by the number (A) squared. 4 squared is 16 and 92064 divided by 16 is 5754. Therefore, B equals 5754.

Once again we have A and B and can get our answer to 92064 in its simplest radical form as follows:

√92064 = A√B

√92064 = 4√5754

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