Question

Give an example for each , if two irrational numbers whose (a) difference is a rational number (b) difference is irrational number (c) sum is a rational number (d) sum is an irrational number (e )Product a rational number (f) Product is an irrational number (g) Quotient is a rational number (h) Quotient is an irrational number

Answer 1

$a) \sqrt{2} - \sqrt{2} \\ b) \sqrt{2 } - \sqrt{3} \\ c) \sqrt{2} + ( - \sqrt{2} ) \\ d) \sqrt{2} + \sqrt{3} \\ e) \sqrt{2} \times \frac{1}{ \sqrt{2} } \\ f) \sqrt{2} \times \sqrt{3} \\ g) \frac{ \sqrt{2} }{ \sqrt{2} } \\ h) \frac{ \sqrt{2} }{ \sqrt{3} }$