No
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pi is a transcendental number, which is a kind of irrational number. That means that the decimal representation of pi does not end (nor does it have a recurring sequence). There is, therefore, no last digit.
It is proven that between two irrational numbers there's an irrational number. There's no method, you just know you can find the number.
The square root of 121 is 11 which is not an irrational number.
No. It is 850000000, which is an integer. An irrational number is one that cannot be expressed as p/q, with p and q integers. 850000000=850000000/1, so it is not irrational.
8 is an integer, which, by definition, are not irrational. In particular, an irrational number is a number that cannot be written in the form p/q for p and q both integers. However, since 8 clearly is equal to 8k/k for any integer k (and for that matter any nonzero number k), 8 is not irrational