Simplify Square Root of 58016

Here we will show you two methods that you can use to simplify the square root of 58016. In other words, we will show you how to find the square root of 58016 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.

√58016 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 58016 to simplify the square root of 58016. 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 58016. The factors of 58016 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 37, 49, 56, 74, 98, 112, 148, 196, 224, 259, 296, 392, 518, 592, 784, 1036, 1184, 1568, 1813, 2072, 3626, 4144, 7252, 8288, 14504, 29008, and 58016. Furthermore, the greatest perfect square on this list is 784 and the square root of 784 is 28. Therefore, A equals 28.

B = Calculate 58016 divided by the greatest perfect square from the list of all factors of 58016. We determined above that the greatest perfect square from the list of all factors of 58016 is 784. Furthermore, 58016 divided by 784 is 74, therefore B equals 74.

Now we have A and B and can get our answer to 58016 in its simplest radical form as follows:

√58016 = A√B

√58016 = 28√74

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 58016 to simplify the square root of 58016 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 58016 and then take the square root of that product. The prime factors that multiply together to make 58016 are 2 x 2 x 2 x 2 x 2 x 7 x 7 x 37. 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 58016 by the number (A) squared. 28 squared is 784 and 58016 divided by 784 is 74. Therefore, B equals 74.

Once again we have A and B and can get our answer to 58016 in its simplest radical form as follows:

√58016 = A√B

√58016 = 28√74

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