Simplify Square Root of 60016

Here we will show you two methods that you can use to simplify the square root of 60016. In other words, we will show you how to find the square root of 60016 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.

√60016 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 60016 to simplify the square root of 60016. 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 60016. The factors of 60016 are 1, 2, 4, 8, 11, 16, 22, 31, 44, 62, 88, 121, 124, 176, 242, 248, 341, 484, 496, 682, 968, 1364, 1936, 2728, 3751, 5456, 7502, 15004, 30008, and 60016. Furthermore, the greatest perfect square on this list is 1936 and the square root of 1936 is 44. Therefore, A equals 44.

B = Calculate 60016 divided by the greatest perfect square from the list of all factors of 60016. We determined above that the greatest perfect square from the list of all factors of 60016 is 1936. Furthermore, 60016 divided by 1936 is 31, therefore B equals 31.

Now we have A and B and can get our answer to 60016 in its simplest radical form as follows:

√60016 = A√B

√60016 = 44√31

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 60016 to simplify the square root of 60016 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 60016 and then take the square root of that product. The prime factors that multiply together to make 60016 are 2 x 2 x 2 x 2 x 11 x 11 x 31. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 11 x 11 = 1936 and the square root of 1936 is 44. Therefore, A equals 44.

B = Divide 60016 by the number (A) squared. 44 squared is 1936 and 60016 divided by 1936 is 31. Therefore, B equals 31.

Once again we have A and B and can get our answer to 60016 in its simplest radical form as follows:

√60016 = A√B

√60016 = 44√31

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