Simplify Square Root of 60648

Here we will show you two methods that you can use to simplify the square root of 60648. In other words, we will show you how to find the square root of 60648 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.

√60648 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 60648 to simplify the square root of 60648. 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 60648. The factors of 60648 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 19, 21, 24, 28, 38, 42, 56, 57, 76, 84, 114, 133, 152, 168, 228, 266, 361, 399, 456, 532, 722, 798, 1064, 1083, 1444, 1596, 2166, 2527, 2888, 3192, 4332, 5054, 7581, 8664, 10108, 15162, 20216, 30324, and 60648. Furthermore, the greatest perfect square on this list is 1444 and the square root of 1444 is 38. Therefore, A equals 38.

B = Calculate 60648 divided by the greatest perfect square from the list of all factors of 60648. We determined above that the greatest perfect square from the list of all factors of 60648 is 1444. Furthermore, 60648 divided by 1444 is 42, therefore B equals 42.

Now we have A and B and can get our answer to 60648 in its simplest radical form as follows:

√60648 = A√B

√60648 = 38√42

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 60648 to simplify the square root of 60648 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 60648 and then take the square root of that product. The prime factors that multiply together to make 60648 are 2 x 2 x 2 x 3 x 7 x 19 x 19. When we strip out the pairs only, we get 2 x 2 x 19 x 19 = 1444 and the square root of 1444 is 38. Therefore, A equals 38.

B = Divide 60648 by the number (A) squared. 38 squared is 1444 and 60648 divided by 1444 is 42. Therefore, B equals 42.

Once again we have A and B and can get our answer to 60648 in its simplest radical form as follows:

√60648 = A√B

√60648 = 38√42

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