Simplify Square Root of 56808

Here we will show you two methods that you can use to simplify the square root of 56808. In other words, we will show you how to find the square root of 56808 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.

√56808 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 56808 to simplify the square root of 56808. 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 56808. The factors of 56808 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216, 263, 526, 789, 1052, 1578, 2104, 2367, 3156, 4734, 6312, 7101, 9468, 14202, 18936, 28404, and 56808. Furthermore, the greatest perfect square on this list is 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Calculate 56808 divided by the greatest perfect square from the list of all factors of 56808. We determined above that the greatest perfect square from the list of all factors of 56808 is 36. Furthermore, 56808 divided by 36 is 1578, therefore B equals 1578.

Now we have A and B and can get our answer to 56808 in its simplest radical form as follows:

√56808 = A√B

√56808 = 6√1578

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 56808 to simplify the square root of 56808 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 56808 and then take the square root of that product. The prime factors that multiply together to make 56808 are 2 x 2 x 2 x 3 x 3 x 3 x 263. 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 56808 by the number (A) squared. 6 squared is 36 and 56808 divided by 36 is 1578. Therefore, B equals 1578.

Once again we have A and B and can get our answer to 56808 in its simplest radical form as follows:

√56808 = A√B

√56808 = 6√1578

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