Simplify Square Root of 25704

Here we will show you two methods that you can use to simplify the square root of 25704. In other words, we will show you how to find the square root of 25704 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.

√25704 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 25704 to simplify the square root of 25704. 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 25704. The factors of 25704 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 17, 18, 21, 24, 27, 28, 34, 36, 42, 51, 54, 56, 63, 68, 72, 84, 102, 108, 119, 126, 136, 153, 168, 189, 204, 216, 238, 252, 306, 357, 378, 408, 459, 476, 504, 612, 714, 756, 918, 952, 1071, 1224, 1428, 1512, 1836, 2142, 2856, 3213, 3672, 4284, 6426, 8568, 12852, and 25704. Furthermore, the greatest perfect square on this list is 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Calculate 25704 divided by the greatest perfect square from the list of all factors of 25704. We determined above that the greatest perfect square from the list of all factors of 25704 is 36. Furthermore, 25704 divided by 36 is 714, therefore B equals 714.

Now we have A and B and can get our answer to 25704 in its simplest radical form as follows:

√25704 = A√B

√25704 = 6√714

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 25704 to simplify the square root of 25704 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 25704 and then take the square root of that product. The prime factors that multiply together to make 25704 are 2 x 2 x 2 x 3 x 3 x 3 x 7 x 17. 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 25704 by the number (A) squared. 6 squared is 36 and 25704 divided by 36 is 714. Therefore, B equals 714.

Once again we have A and B and can get our answer to 25704 in its simplest radical form as follows:

√25704 = A√B

√25704 = 6√714

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