Set 1.1 Questions 56-59 David Cohen In Exercises 56–58, give an example of irrational numbers a and b such that the indicated expression is (a) rational and (b) irrational. 56. a + b sqrt{4} + sqrt{9} = 2 + 3 = 5 = rational. sqrt16} + sqrt{2} = 4 + sqrt{2} = irrational. Yes? 57. a•b sqrt{2}•sqrt{2} = sqrt{4} = 2 = rational. sqrt{3}•sqrt{7} = sqrt{21} = irrational. Yes? 58. a/b sqrt{9}/sqrt{81} = 3/9 = 1/3 = rational. sqrt{2}/sqrt{3} = sqrt{6}/sqrt{9} = sqrt{6}/3 = irrational. Yes? 59. (a) Give an example in which the result of raising a rational number to a rational power is an irrational number. How about 3^(1/4)? (b) Give an example in which the result of raising an irrational number to a rational power is a rational number. How about [sqrt{2}]^2? You say?
