Simplify Square Root of 57708

Here we will show you two methods that you can use to simplify the square root of 57708. In other words, we will show you how to find the square root of 57708 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.

√57708 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 57708 to simplify the square root of 57708. 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 57708. The factors of 57708 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 229, 252, 458, 687, 916, 1374, 1603, 2061, 2748, 3206, 4122, 4809, 6412, 8244, 9618, 14427, 19236, 28854, and 57708. Furthermore, the greatest perfect square on this list is 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Calculate 57708 divided by the greatest perfect square from the list of all factors of 57708. We determined above that the greatest perfect square from the list of all factors of 57708 is 36. Furthermore, 57708 divided by 36 is 1603, therefore B equals 1603.

Now we have A and B and can get our answer to 57708 in its simplest radical form as follows:

√57708 = A√B

√57708 = 6√1603

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 57708 to simplify the square root of 57708 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 57708 and then take the square root of that product. The prime factors that multiply together to make 57708 are 2 x 2 x 3 x 3 x 7 x 229. 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 57708 by the number (A) squared. 6 squared is 36 and 57708 divided by 36 is 1603. Therefore, B equals 1603.

Once again we have A and B and can get our answer to 57708 in its simplest radical form as follows:

√57708 = A√B

√57708 = 6√1603

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