Answer :

(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 in the form

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)

∵ is irrational number and addition of an irrational number to any real number always gives irrational number.

Hence, it is an irrational number.

(vi)

∵ is irrational number and addition of an irrational number to any real number always gives irrational number.

Hence, it is an irrational number.

(vii)

=

∵ As, and √2 are irrational numbers and multiplication of an irrational number to a non zero rational number gives irrational number.

Hence, it is an irrational number.

(viii)

∵ we know that all repeating decimals are rational,

Hence, it is a rational number.

(ix) 1.232332333…

∵ The decimal expansion here is non terminating and non repeating,

Hence, it is an irrational number.

(x) 3.040040004…

∵ The decimal expansion here is non terminating and non repeating,

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 non terminating but 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.

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