Simplify Square Root of 55660

Here we will show you two methods that you can use to simplify the square root of 55660. In other words, we will show you how to find the square root of 55660 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.

√55660 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 55660 to simplify the square root of 55660. 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 55660. The factors of 55660 are 1, 2, 4, 5, 10, 11, 20, 22, 23, 44, 46, 55, 92, 110, 115, 121, 220, 230, 242, 253, 460, 484, 506, 605, 1012, 1210, 1265, 2420, 2530, 2783, 5060, 5566, 11132, 13915, 27830, and 55660. Furthermore, the greatest perfect square on this list is 484 and the square root of 484 is 22. Therefore, A equals 22.

B = Calculate 55660 divided by the greatest perfect square from the list of all factors of 55660. We determined above that the greatest perfect square from the list of all factors of 55660 is 484. Furthermore, 55660 divided by 484 is 115, therefore B equals 115.

Now we have A and B and can get our answer to 55660 in its simplest radical form as follows:

√55660 = A√B

√55660 = 22√115

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 55660 to simplify the square root of 55660 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 55660 and then take the square root of that product. The prime factors that multiply together to make 55660 are 2 x 2 x 5 x 11 x 11 x 23. When we strip out the pairs only, we get 2 x 2 x 11 x 11 = 484 and the square root of 484 is 22. Therefore, A equals 22.

B = Divide 55660 by the number (A) squared. 22 squared is 484 and 55660 divided by 484 is 115. Therefore, B equals 115.

Once again we have A and B and can get our answer to 55660 in its simplest radical form as follows:

√55660 = A√B

√55660 = 22√115

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