Simplify Square Root of 95744

Here we will show you two methods that you can use to simplify the square root of 95744. In other words, we will show you how to find the square root of 95744 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.

√95744 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 95744 to simplify the square root of 95744. 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 95744. The factors of 95744 are 1, 2, 4, 8, 11, 16, 17, 22, 32, 34, 44, 64, 68, 88, 128, 136, 176, 187, 256, 272, 352, 374, 512, 544, 704, 748, 1088, 1408, 1496, 2176, 2816, 2992, 4352, 5632, 5984, 8704, 11968, 23936, 47872, and 95744. Furthermore, the greatest perfect square on this list is 256 and the square root of 256 is 16. Therefore, A equals 16.

B = Calculate 95744 divided by the greatest perfect square from the list of all factors of 95744. We determined above that the greatest perfect square from the list of all factors of 95744 is 256. Furthermore, 95744 divided by 256 is 374, therefore B equals 374.

Now we have A and B and can get our answer to 95744 in its simplest radical form as follows:

√95744 = A√B

√95744 = 16√374

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 95744 to simplify the square root of 95744 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 95744 and then take the square root of that product. The prime factors that multiply together to make 95744 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 11 x 17. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 256 and the square root of 256 is 16. Therefore, A equals 16.

B = Divide 95744 by the number (A) squared. 16 squared is 256 and 95744 divided by 256 is 374. Therefore, B equals 374.

Once again we have A and B and can get our answer to 95744 in its simplest radical form as follows:

√95744 = A√B

√95744 = 16√374

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

Simplify Square Root of 95745
Here is the next square root on our list that we have simplifed for you.