If you have any positive irrational number, then its negative is also irrational.
A negative irrational number can be thought of as an irrational number multiplied by -1, or an irrational number with a minus sign in front of it.
If it says "negative irrational", then obviously it is irrational.
No, it is not irrational because it is a square root of a negative number - which falls into the set of Complex numbers. Irrational numbers can not have an imaginary component.
The negative of a rational number is also rational.
Not necessarily. Irrational numbers can be negative or positive.
No integer is irrational.
No, they can be rational or irrational. The sign of a number has nothing to do with it.
Unless the integer is fractional it is not an irrational number.