Simplify Square Root of 2556

Here we will show you two methods that you can use to simplify the square root of 2556. In other words, we will show you how to find the square root of 2556 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.

√2556 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 2556 to simplify the square root of 2556. 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 2556. The factors of 2556 are 1, 2, 3, 4, 6, 9, 12, 18, 36, 71, 142, 213, 284, 426, 639, 852, 1278, and 2556. Furthermore, the greatest perfect square on this list is 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Calculate 2556 divided by the greatest perfect square from the list of all factors of 2556. We determined above that the greatest perfect square from the list of all factors of 2556 is 36. Furthermore, 2556 divided by 36 is 71, therefore B equals 71.

Now we have A and B and can get our answer to 2556 in its simplest radical form as follows:

√2556 = A√B

√2556 = 6√71

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 2556 to simplify the square root of 2556 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 2556 and then take the square root of that product. The prime factors that multiply together to make 2556 are 2 x 2 x 3 x 3 x 71. When we strip out the pairs only, we get 2 x 2 x 3 x 3 = 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Divide 2556 by the number (A) squared. 6 squared is 36 and 2556 divided by 36 is 71. Therefore, B equals 71.

Once again we have A and B and can get our answer to 2556 in its simplest radical form as follows:

√2556 = A√B

√2556 = 6√71

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Simplify Square Root of 2557
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