  Question

Give an example of each, of two irrational numbers whose: (i) difference is a rational number. (ii) difference is an irrational number. (iii) sum is a rational number. (iv) sum is an irrational number. (v) product is an rational number. (vi) product is an irrational number. (vii) quotient is a rational number. (viii) quotient is an irrational number.

Solution

(i) Let And, so Therefore, and are two irrational numbers and their difference is a rational number (ii) Let are two irrational numbers and their difference is an irrational number Because is an irrational number (iii) Let are two irrational numbers and their sum is a rational number That is (iv) Let are two irrational numbers and their sum is an irrational number  That is (v) Let are two irrational numbers and their product is a rational number That is (vi) Let are two irrational numbers and their product is an irrational number That is (vii) Let are two irrational numbers and their quotient is a rational number That is (viii) Let are two irrational numbers and their quotient is an irrational number That is MathematicsRD Sharma (2017)Standard IX

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