Simplify Square Root of 60123

Here we will show you two methods that you can use to simplify the square root of 60123. In other words, we will show you how to find the square root of 60123 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.

√60123 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 60123 to simplify the square root of 60123. 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 60123. The factors of 60123 are 1, 3, 7, 21, 49, 147, 409, 1227, 2863, 8589, 20041, and 60123. Furthermore, the greatest perfect square on this list is 49 and the square root of 49 is 7. Therefore, A equals 7.

B = Calculate 60123 divided by the greatest perfect square from the list of all factors of 60123. We determined above that the greatest perfect square from the list of all factors of 60123 is 49. Furthermore, 60123 divided by 49 is 1227, therefore B equals 1227.

Now we have A and B and can get our answer to 60123 in its simplest radical form as follows:

√60123 = A√B

√60123 = 7√1227

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 60123 to simplify the square root of 60123 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 60123 and then take the square root of that product. The prime factors that multiply together to make 60123 are 3 x 7 x 7 x 409. When we strip out the pairs only, we get 7 x 7 = 49 and the square root of 49 is 7. Therefore, A equals 7.

B = Divide 60123 by the number (A) squared. 7 squared is 49 and 60123 divided by 49 is 1227. Therefore, B equals 1227.

Once again we have A and B and can get our answer to 60123 in its simplest radical form as follows:

√60123 = A√B

√60123 = 7√1227

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

Simplify Square Root of 60124
Here is the next square root on our list that we have simplifed for you.