Simplify Square Root of 60400

Here we will show you two methods that you can use to simplify the square root of 60400. In other words, we will show you how to find the square root of 60400 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.

√60400 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 60400 to simplify the square root of 60400. 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 60400. The factors of 60400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 151, 200, 302, 400, 604, 755, 1208, 1510, 2416, 3020, 3775, 6040, 7550, 12080, 15100, 30200, and 60400. Furthermore, the greatest perfect square on this list is 400 and the square root of 400 is 20. Therefore, A equals 20.

B = Calculate 60400 divided by the greatest perfect square from the list of all factors of 60400. We determined above that the greatest perfect square from the list of all factors of 60400 is 400. Furthermore, 60400 divided by 400 is 151, therefore B equals 151.

Now we have A and B and can get our answer to 60400 in its simplest radical form as follows:

√60400 = A√B

√60400 = 20√151

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 60400 to simplify the square root of 60400 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 60400 and then take the square root of that product. The prime factors that multiply together to make 60400 are 2 x 2 x 2 x 2 x 5 x 5 x 151. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 5 x 5 = 400 and the square root of 400 is 20. Therefore, A equals 20.

B = Divide 60400 by the number (A) squared. 20 squared is 400 and 60400 divided by 400 is 151. Therefore, B equals 151.

Once again we have A and B and can get our answer to 60400 in its simplest radical form as follows:

√60400 = A√B

√60400 = 20√151

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

Simplify Square Root of 60401
Here is the next square root on our list that we have simplifed for you.