Question

Justify: a. The difference of 2 irrational numbers is irrational

Answer 1

Let the 2 irrational numbers be √3, √5 and difference is √3-√5
√3 -√5 = p/q (assume that difference between √3 and √5 i rational i.e., p/q)
squaring on both sides 
(√3-√5)² = (p/q)²
(√3)² + (√5)² - 2×√3×√5 = p²/q²
3+5-2√15 = p²/q²
8-2√15 = p²/q²
2√15 = 8-p²/q²
Since 8-p²/q² is rational, 2√15 also must be rational
but 2√15 is an irrational number
this contradicts the fact that 2√15 is an irrational number and our assumption is wrong
hence, the difference between any 2 irrational number is an irrational number only.