Simplify Square Root of 74880

Here we will show you two methods that you can use to simplify the square root of 74880. In other words, we will show you how to find the square root of 74880 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.

√74880 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 74880 to simplify the square root of 74880. 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 74880. The factors of 74880 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15, 16, 18, 20, 24, 26, 30, 32, 36, 39, 40, 45, 48, 52, 60, 64, 65, 72, 78, 80, 90, 96, 104, 117, 120, 128, 130, 144, 156, 160, 180, 192, 195, 208, 234, 240, 260, 288, 312, 320, 360, 384, 390, 416, 468, 480, 520, 576, 585, 624, 640, 720, 780, 832, 936, 960, 1040, 1152, 1170, 1248, 1440, 1560, 1664, 1872, 1920, 2080, 2340, 2496, 2880, 3120, 3744, 4160, 4680, 4992, 5760, 6240, 7488, 8320, 9360, 12480, 14976, 18720, 24960, 37440, and 74880. Furthermore, the greatest perfect square on this list is 576 and the square root of 576 is 24. Therefore, A equals 24.

B = Calculate 74880 divided by the greatest perfect square from the list of all factors of 74880. We determined above that the greatest perfect square from the list of all factors of 74880 is 576. Furthermore, 74880 divided by 576 is 130, therefore B equals 130.

Now we have A and B and can get our answer to 74880 in its simplest radical form as follows:

√74880 = A√B

√74880 = 24√130

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 74880 to simplify the square root of 74880 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 74880 and then take the square root of that product. The prime factors that multiply together to make 74880 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 13. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 = 576 and the square root of 576 is 24. Therefore, A equals 24.

B = Divide 74880 by the number (A) squared. 24 squared is 576 and 74880 divided by 576 is 130. Therefore, B equals 130.

Once again we have A and B and can get our answer to 74880 in its simplest radical form as follows:

√74880 = A√B

√74880 = 24√130

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

Simplify Square Root of 74881
Here is the next square root on our list that we have simplifed for you.