There are an infinite number of them. One of them is
[ the square root of(0.0000000100001) ]
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anything that starts with 5.1... and goes on forever without repeating such as 5.17487568454857563475678578574384754 =)
It is bigger
5.7 squared is 32.49 and 5.72 squared is 32.7184. Therefore the square root of number between 32.49 and 32.7184 is between 5.7 and 5.72 and probably irrational. One example is the square root of 32.6 which is about 5.70964...
The sum of a rational and irrational number must be an irrational number.
No, 3.56 is not an irrational number. 3.56 is rational.