The square root of 2.56 is rational. This is because 2.56 can be expressed as 256/100, which simplifies to 64/25. The square root of 64 is 8 and the square root of 25 is 5, so the square root of 2.56 is 8/5, which is a rational number.
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4th root is same as square root of square root: sqrt(256) = 16, and sqrt(16) = 4
16.
16 x 16 = 256
The idea is to take out perfect squares. The largest perfect square in this case is 256, which is the square of 16 (if you have trouble figuring this out, you can take out a smaller perfect square first, and then see if you find additional perfect squares). In any case, the end result should not have a factor that is a perfect square. Using the symbol "root()" for square root: root(512) = root(256 x 2) = root(256) x root(2) = 16 root(2)
It has no pure square root. 16 x 16 =256 but this leaves a remainder of 24.