(i) 2 - √5

We kno that √5 = 2.236..., which is an irrational number

2 - √5 = 2 - 2.236..

= -0.236..., which is also an irrational number.

Therefore, we conclude that 2 - √5 is an irrational number.

(ii) (3 +√23) - √23

(3 +√23) - √23 = 3 +√23 - √23 = 3.

Therefore, we conclude that (3 +√23) - √23 is a rational number

(iii) ** 2√7/7√7**

We can cancel **√7 **n the numerator and denominator, as **√****7 is the **the common number in numerator as well as denominator, to get

**2√7/7√7 = 2/7**

**Therefore, we conclude that 2√7/7√7 is rational number.**