Simplify Square Root of 59840

Here we will show you two methods that you can use to simplify the square root of 59840. In other words, we will show you how to find the square root of 59840 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.

√59840 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 59840 to simplify the square root of 59840. 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 59840. The factors of 59840 are 1, 2, 4, 5, 8, 10, 11, 16, 17, 20, 22, 32, 34, 40, 44, 55, 64, 68, 80, 85, 88, 110, 136, 160, 170, 176, 187, 220, 272, 320, 340, 352, 374, 440, 544, 680, 704, 748, 880, 935, 1088, 1360, 1496, 1760, 1870, 2720, 2992, 3520, 3740, 5440, 5984, 7480, 11968, 14960, 29920, and 59840. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 59840 divided by the greatest perfect square from the list of all factors of 59840. We determined above that the greatest perfect square from the list of all factors of 59840 is 64. Furthermore, 59840 divided by 64 is 935, therefore B equals 935.

Now we have A and B and can get our answer to 59840 in its simplest radical form as follows:

√59840 = A√B

√59840 = 8√935

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 59840 to simplify the square root of 59840 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 59840 and then take the square root of that product. The prime factors that multiply together to make 59840 are 2 x 2 x 2 x 2 x 2 x 2 x 5 x 11 x 17. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 = 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Divide 59840 by the number (A) squared. 8 squared is 64 and 59840 divided by 64 is 935. Therefore, B equals 935.

Once again we have A and B and can get our answer to 59840 in its simplest radical form as follows:

√59840 = A√B

√59840 = 8√935

Simplify Square Root
Please enter another square root in the box below for us to simplify.

Simplify Square Root of 59841
Here is the next square root on our list that we have simplifed for you.