Classify the following numbers as rational or irrational: (i). 2 - √5
(ii). (3 + √23) - √23
(iii). (2√7) / (7√7)
(iv). 1 / √2
(v). 2π

Let's classify each number as rational or irrational:

(i) 2 - √5:

The number 2 is rational, and √5 is an irrational number.
The difference between a rational number and an irrational number is always irrational.
Therefore, 2 - √5 is an irrational number.
(ii) (3 + √23) - √23:

Simplifying the expression: (3 + √23) - √23 = 3.
The number 3 is a rational number.
Therefore, (3 + √23) - √23 is a rational number.
(iii) (2√7) / (7√7):

Simplifying the expression: (2√7) / (7√7) = 2 / 7.
The number 2/7 is a rational number because it is the ratio of two integers.
Therefore, (2√7) / (7√7) is a rational number.
(iv) 1 / √2:

√2 is an irrational number.
The reciprocal of an irrational number (such as 1/√2) is also irrational.
Therefore, 1 / √2 is an irrational number.
(v) 2π:

π is an irrational number.
The product of a rational number (2) and an irrational number (π) is irrational.
Therefore, 2π is an irrational number.
Summary: (i) Irrational
(ii) Rational
(iii) Rational
(iv) Irrational
(v) Irrational