Simplify Square Root of 55856

Here we will show you two methods that you can use to simplify the square root of 55856. In other words, we will show you how to find the square root of 55856 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.

√55856 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 55856 to simplify the square root of 55856. 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 55856. The factors of 55856 are 1, 2, 4, 8, 16, 3491, 6982, 13964, 27928, and 55856. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 55856 divided by the greatest perfect square from the list of all factors of 55856. We determined above that the greatest perfect square from the list of all factors of 55856 is 16. Furthermore, 55856 divided by 16 is 3491, therefore B equals 3491.

Now we have A and B and can get our answer to 55856 in its simplest radical form as follows:

√55856 = A√B

√55856 = 4√3491

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 55856 to simplify the square root of 55856 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 55856 and then take the square root of that product. The prime factors that multiply together to make 55856 are 2 x 2 x 2 x 2 x 3491. When we strip out the pairs only, we get 2 x 2 x 2 x 2 = 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Divide 55856 by the number (A) squared. 4 squared is 16 and 55856 divided by 16 is 3491. Therefore, B equals 3491.

Once again we have A and B and can get our answer to 55856 in its simplest radical form as follows:

√55856 = A√B

√55856 = 4√3491

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Simplify Square Root of 55857
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