Examples for addition or subtration of irration numbers?

Answer 1

Irrational nos. when added, subtracted produce another irrational number. Thus the set of Irrational Numbers is said to be closed with respect to addition and subtraction. examples of addition: Here I quote the addition of two surds: sqrt(2)+sqrt(5) where sqrt(x) denotes square root of the number x examples of subtraction: pi-sqrt(7)+13.345678342698754123597643565456654445.......... here pi denotes the irrational no. pi(approx. 3.1415927) and the other number is a non repeating, non terminating decimally expanding number and is hence irrational. Their difference is also irrational. Note that a number like 3.3434343434...... where the decimal digits repeat is purely rational since the decimal expansion is repeating, though non terminating. Also, the sum of a positive rational and an irrational number is always irrational, which is not true for subtraction of irational number(example sqrt(5)-sqrt(5)=0, 0 is rational while sqrt(5) is irrational)