Question

Give two irrational numbers so that their.
(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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Solution
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(i) Consider the two irrational number and .
Their sum is an irrational number.
(ii) Consider the two irrational numbers and .
Their sum is a rational number.
(iii) Consider the two irrational numbers and .
Their difference is an irrational number.
(iv) Consider the two irrational numbers and .
Their difference is a rational number.
(v) Consider the two irrational numbers and .
Their product is an irrational number.
(vi) Consider the two irrational numbers and .
Their product is a rational number.
(vii) Consider the two irrational numbers and .
Their quotient is an irrational number.
(viii) Consider the two irrational numbers and .
Their quotient is a rational number.

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