(i) True.
(ii) True.
(iii) False.
Reason:
Sum of two irrational can be rational. Let us take an example,
Consider two irrational numbers: (3 + √2) and (3 – √2)
Sum: (3 + √2) + (3 – √2) = 3 + √2 + 3 – √2 = 6 which is rational.
(iv) False.
Reason:
Product of two irrational numbers can be rational. Let us take an example,
Consider two irrational numbers: (3 + √2) and (3 – √2)
Product: (3 + √2)(3 – √2 )
= (3)2 – (√2 )2
= 9 – 2 = 7; which is rational
(v) True.
(vi) True.