(i)

=

∵ we can express 2 as which is the quotient of the integer 2 and 1

Hence, it is a rational number.

(ii)

=

∵ we can express 14 as which is the quotient of the integer 14 and 1

Hence, it is a rational number.

(iii)

=

∵we can not simplify

Hence, it is an irrational number.

(iv)

We know that 43 is a prime number so we can not get prime factors of it and neither we can write in fractional form.

Hence, it is an irrational number.

(v)

∵ we can not simplify or in integer form,

Hence, it is an irrational number.

(vi)

∵ we can not simplify or in integer form,

Hence, it is an irrational number.

(vii)

=

∵ we can not simplify or √2 in integer form,

Hence, it is an irrational number.

(viii)

∵ we know that all repeating decimals are rational,

Hence, it is a rational number.

(ix) 1.232332333…

∵ we know that non-terminating decimals never repeats and cannot be represented as a quotient of two integers,

Hence, it is an irrational number.

(x) 3.040040004…

∵ we know that non terminating decimals never repeats and can not be represented as a quotient of two integers,

Hence, it is an irrational number.

(xi) 3.2576

∵ It is a terminating decimal fraction and can be expressed in form

Hence it is a rational number.

(xii) 2.3565656…

∵ it is a terminating repeating decimal form that can be written as 2.35.

Hence, it is a rational number.

(xiii)

∵ We know that π is a non terminating Decimal fraction,

Hence it is an irrational number.

(xiv)

∵ it is an fractional form,

Hence it is rational.