Simplify Square Root of 75240

Here we will show you two methods that you can use to simplify the square root of 75240. In other words, we will show you how to find the square root of 75240 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.

√75240 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 75240 to simplify the square root of 75240. 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 75240. The factors of 75240 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 18, 19, 20, 22, 24, 30, 33, 36, 38, 40, 44, 45, 55, 57, 60, 66, 72, 76, 88, 90, 95, 99, 110, 114, 120, 132, 152, 165, 171, 180, 190, 198, 209, 220, 228, 264, 285, 330, 342, 360, 380, 396, 418, 440, 456, 495, 570, 627, 660, 684, 760, 792, 836, 855, 990, 1045, 1140, 1254, 1320, 1368, 1672, 1710, 1881, 1980, 2090, 2280, 2508, 3135, 3420, 3762, 3960, 4180, 5016, 6270, 6840, 7524, 8360, 9405, 12540, 15048, 18810, 25080, 37620, and 75240. Furthermore, the greatest perfect square on this list is 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Calculate 75240 divided by the greatest perfect square from the list of all factors of 75240. We determined above that the greatest perfect square from the list of all factors of 75240 is 36. Furthermore, 75240 divided by 36 is 2090, therefore B equals 2090.

Now we have A and B and can get our answer to 75240 in its simplest radical form as follows:

√75240 = A√B

√75240 = 6√2090

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 75240 to simplify the square root of 75240 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 75240 and then take the square root of that product. The prime factors that multiply together to make 75240 are 2 x 2 x 2 x 3 x 3 x 5 x 11 x 19. When we strip out the pairs only, we get 2 x 2 x 3 x 3 = 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Divide 75240 by the number (A) squared. 6 squared is 36 and 75240 divided by 36 is 2090. Therefore, B equals 2090.

Once again we have A and B and can get our answer to 75240 in its simplest radical form as follows:

√75240 = A√B

√75240 = 6√2090

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

Simplify Square Root of 75241
Here is the next square root on our list that we have simplifed for you.