# Give an example of two irrational numbers whose

Question:

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

Solution:

(i) 2 irrational numbers with difference an irrational number will be $3-\sqrt{5}$ and $3+\sqrt{5}$.

(ii) 2 irrational numbers with difference is a rational number will be $5+\sqrt{3}$ and $2+\sqrt{3}$

(iii) 2 irrational numbers with sum an irrational number $7+\sqrt{5}$ and $\sqrt{6}-8$

(iv) 2 irrational numbers with sum a rational number is $3-\sqrt{2}$ and $3+\sqrt{2}$

(v) 2 irrational numbers with product an irrational number will be $6+\sqrt{3}$ and $7-\sqrt{3}$

(vi) 2 irrational numbers with product a rational number will be $(5+\sqrt{7})$ and $(5-\sqrt{7})$

(vii) 2 irrational numbers with quotient an irrational number will be $\sqrt{15}$ and $\sqrt{5}$

(viii) 2 irrational numbers with quotient a rational number will be $\sqrt{63}$ and $\sqrt{7}$.