Simplify Square Root of 54760

Here we will show you two methods that you can use to simplify the square root of 54760. In other words, we will show you how to find the square root of 54760 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.

√54760 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 54760 to simplify the square root of 54760. 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 54760. The factors of 54760 are 1, 2, 4, 5, 8, 10, 20, 37, 40, 74, 148, 185, 296, 370, 740, 1369, 1480, 2738, 5476, 6845, 10952, 13690, 27380, and 54760. Furthermore, the greatest perfect square on this list is 5476 and the square root of 5476 is 74. Therefore, A equals 74.

B = Calculate 54760 divided by the greatest perfect square from the list of all factors of 54760. We determined above that the greatest perfect square from the list of all factors of 54760 is 5476. Furthermore, 54760 divided by 5476 is 10, therefore B equals 10.

Now we have A and B and can get our answer to 54760 in its simplest radical form as follows:

√54760 = A√B

√54760 = 74√10

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 54760 to simplify the square root of 54760 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 54760 and then take the square root of that product. The prime factors that multiply together to make 54760 are 2 x 2 x 2 x 5 x 37 x 37. When we strip out the pairs only, we get 2 x 2 x 37 x 37 = 5476 and the square root of 5476 is 74. Therefore, A equals 74.

B = Divide 54760 by the number (A) squared. 74 squared is 5476 and 54760 divided by 5476 is 10. Therefore, B equals 10.

Once again we have A and B and can get our answer to 54760 in its simplest radical form as follows:

√54760 = A√B

√54760 = 74√10

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

Simplify Square Root of 54761
Here is the next square root on our list that we have simplifed for you.