Question

(i) sum is an irrational number.

(ii) sum is not an irrational number.

(iii) difference is an irrational number.

(iv) difference is not an irrational number.

(v) product is an irrational number.

(vi) product is not an irrational number.

(vii) quotient is an irrational number.

(viii) quotient is not an irrational number.

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Their sum $=2+3β+3ββ2=23β$ is an irrational number.

(ii) Consider the two irrational numbers $2β$ and $β2β$.

Their sum $=2β+(β2β)=0$ is a rational number.

(iii) Consider the two irrational numbers $3β$ and $2β$.

Their difference$=3ββ2β$ is an irrational number.

(iv) Consider the two irrational numbers $5+3β$ and $3ββ5$.

Their difference $=(5+3β)β(3ββ5)=10$ is a rational number.

(v) Consider the two irrational numbers $3β$ and $5β$.

Their product $=3βΓ5β=15β$ is an irrational number.

(vi) Consider the two irrational numbers $18β$ and $2β$.

Their product $=18βΓ2β=36β=6$ is a rational number.

(vii) Consider the two irrational numbers $15β$ and $3β$.

Their quotient $=3β15ββ=315ββ=5β$ is an irrational number.

(viii) Consider the two irrational numbers $75β$ and $3β$.

Their quotient $=3β75ββ=375ββ=5$ is a rational number.

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