Which of the following are irrational numbers?

i. ii.

iii. iv.

i.√(2 + √3 ) is irrational ∵ √3 is irrational and 2 is rational and sum of a rational and irrational number is always irrational. Hence 2 + √3 is irrational. Hence, its square root is also irrational.

ii.√(4 + √25) is rational ∵ √25( = 5) is rational and 4 is also rational.

Hence, √(4 + 5) = √9 = 3 is rational.

iii. ∛(5 + √7) is irrational ∵ √7 is irrational and 5 is rational and sum of a rational and irrational number is always irrational. Hence 5 + √7 is irrational. Hence, its cube root is also irrational.

iv.√(8-∛8 ) is irrational. Here both ( = 2) and 8 are rational. Hence

8 – 8^1/3 = 8 – 2 = 6 is rational. But √6 is irrational.

Hence, the answer.