Simplify Square Root of 75295

Here we will show you two methods that you can use to simplify the square root of 75295. In other words, we will show you how to find the square root of 75295 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.

√75295 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 75295 to simplify the square root of 75295. 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 75295. The factors of 75295 are 1, 5, 11, 37, 55, 185, 407, 1369, 2035, 6845, 15059, and 75295. Furthermore, the greatest perfect square on this list is 1369 and the square root of 1369 is 37. Therefore, A equals 37.

B = Calculate 75295 divided by the greatest perfect square from the list of all factors of 75295. We determined above that the greatest perfect square from the list of all factors of 75295 is 1369. Furthermore, 75295 divided by 1369 is 55, therefore B equals 55.

Now we have A and B and can get our answer to 75295 in its simplest radical form as follows:

√75295 = A√B

√75295 = 37√55

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 75295 to simplify the square root of 75295 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 75295 and then take the square root of that product. The prime factors that multiply together to make 75295 are 5 x 11 x 37 x 37. When we strip out the pairs only, we get 37 x 37 = 1369 and the square root of 1369 is 37. Therefore, A equals 37.

B = Divide 75295 by the number (A) squared. 37 squared is 1369 and 75295 divided by 1369 is 55. Therefore, B equals 55.

Once again we have A and B and can get our answer to 75295 in its simplest radical form as follows:

√75295 = A√B

√75295 = 37√55

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

Simplify Square Root of 75296
Here is the next square root on our list that we have simplifed for you.