Simplify Square Root of 74294

Here we will show you two methods that you can use to simplify the square root of 74294. In other words, we will show you how to find the square root of 74294 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.

√74294 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 74294 to simplify the square root of 74294. 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 74294. The factors of 74294 are 1, 2, 11, 22, 121, 242, 307, 614, 3377, 6754, 37147, and 74294. Furthermore, the greatest perfect square on this list is 121 and the square root of 121 is 11. Therefore, A equals 11.

B = Calculate 74294 divided by the greatest perfect square from the list of all factors of 74294. We determined above that the greatest perfect square from the list of all factors of 74294 is 121. Furthermore, 74294 divided by 121 is 614, therefore B equals 614.

Now we have A and B and can get our answer to 74294 in its simplest radical form as follows:

√74294 = A√B

√74294 = 11√614

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 74294 to simplify the square root of 74294 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 74294 and then take the square root of that product. The prime factors that multiply together to make 74294 are 2 x 11 x 11 x 307. When we strip out the pairs only, we get 11 x 11 = 121 and the square root of 121 is 11. Therefore, A equals 11.

B = Divide 74294 by the number (A) squared. 11 squared is 121 and 74294 divided by 121 is 614. Therefore, B equals 614.

Once again we have A and B and can get our answer to 74294 in its simplest radical form as follows:

√74294 = A√B

√74294 = 11√614

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

Simplify Square Root of 74295
Here is the next square root on our list that we have simplifed for you.