No.
The sum of an irrational number and any other [real] number is irrational.
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Yes
10+0.01 = 10.01 and it is a rational number
It is a rational number.
If an irrational number is added to, (or multiplied by) a rational number, the result will always be an irrational number.
When a rational numbers is divided by an irrational number, the answer is irrational for every non-zero rational number.