State which of the following numbers are rational and irrational.

i. 2-√5

ii. (3 + √23)-√23

iii.

iv.

v. 5π

i. 2-√5

Since √5 is an irrational number

⇒ 2 - √5 is irrational number.

ii. (3 + √23)-√23

(3 + √23)-√23

= 3

Since 3 is rational

⇒ (3 + √23)-√23is rational number.

iii.

=

Since is rational

⇒ is rational

iv.

Rationalizing we get,

Since is irrational

⇒ is irrational.

v. 5π

Since is irrational

⇒ is irrational.