No. 5.6 is rational.
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No, it is rational 56/7 = 8 which is rational
72 = 49 and 82 = 64. So, the square root of any integer between these two numbers, for example, sqrt(56), is irrational.
The question could ask for the perfect cube of 56, which equals 563 = 175616. However, it can also mean to ask whether 56 can be a cube, which could be answered by 56(1/3), which cubed is 56. Since 56(1/3) is an irrational number, it is impossible to construct this perfectly, but one can make arbitrary precise approximations, close to 3.825862365...
yes
Yes. The sum of two irrational numbers can be rational, or irrational.