Simplify Square Root of 60112

Here we will show you two methods that you can use to simplify the square root of 60112. In other words, we will show you how to find the square root of 60112 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.

√60112 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 60112 to simplify the square root of 60112. 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 60112. The factors of 60112 are 1, 2, 4, 8, 13, 16, 17, 26, 34, 52, 68, 104, 136, 208, 221, 272, 289, 442, 578, 884, 1156, 1768, 2312, 3536, 3757, 4624, 7514, 15028, 30056, and 60112. Furthermore, the greatest perfect square on this list is 4624 and the square root of 4624 is 68. Therefore, A equals 68.

B = Calculate 60112 divided by the greatest perfect square from the list of all factors of 60112. We determined above that the greatest perfect square from the list of all factors of 60112 is 4624. Furthermore, 60112 divided by 4624 is 13, therefore B equals 13.

Now we have A and B and can get our answer to 60112 in its simplest radical form as follows:

√60112 = A√B

√60112 = 68√13

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 60112 to simplify the square root of 60112 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 60112 and then take the square root of that product. The prime factors that multiply together to make 60112 are 2 x 2 x 2 x 2 x 13 x 17 x 17. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 17 x 17 = 4624 and the square root of 4624 is 68. Therefore, A equals 68.

B = Divide 60112 by the number (A) squared. 68 squared is 4624 and 60112 divided by 4624 is 13. Therefore, B equals 13.

Once again we have A and B and can get our answer to 60112 in its simplest radical form as follows:

√60112 = A√B

√60112 = 68√13

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