Classify each of the following as a rational or irrational number

(a)square root 2+8
(b)7/22
(c)3.14114111411114..

To classify each of the following as a rational or irrational number, we need to understand the definitions of rational and irrational numbers.

A rational number is any number that can be expressed as the ratio of two integers (where the denominator is not zero). It can be written in the form p/q, where p and q are integers.

An irrational number is any number that cannot be expressed as the ratio of two integers. It cannot be written in the form p/q, where p and q are integers.

Now let's classify each of the given numbers:

(a) Square root of 2 + 8:
The square root of 2 is an irrational number because it cannot be expressed as the ratio of two integers. Adding 8 to an irrational number doesn't change its classification. Therefore, square root of 2 + 8 is an irrational number.

(b) 7/22:
7/22 is a rational number because it can be expressed as the ratio of two integers (7 and 22). The numerator and denominator are both integers, and the denominator is not zero.

(c) 3.14114111411114...:
The given number seems to be a decimal representation of the irrational number pi (π). The decimals continue indefinitely without repeating. Since pi cannot be expressed as the ratio of two integers, it is an irrational number.

To summarize:
(a) Square root of 2 + 8 is an irrational number.
(b) 7/22 is a rational number.
(c) 3.14114111411114... (pi) is an irrational number.