Rational & Irrational Numbers

[nycmathguy]

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?

 

[MathLover1]

56.

correct

57.

correct

58.
correct

59.
a) correct
b) correct

way to go!

 

[nycmathguy]

56.

correct

57.

correct

58.
correct

59.
a) correct
b) correct

way to go!

I'm cooking with gas now. This is a famous Richie line from Happy Days.

 

[HallsofIvy]

NO! Whether a number is rational or irrational is a property of the number, not how it is expressed!
sqrt(4)= 2 is a rational number NOT an irrational number. sqrt(9)= 3 is a rational number, not an irrational number.

 

[MathLover1]

NO! Whether a number is rational or irrational is a property of the number, not how it is expressed!
sqrt(4)= 2 is a rational number NOT an irrational number. sqrt(9)= 3 is a rational number, not an irrational number.

omg, you are right, he needed to add two irrational numbers a and b to get rational

 

[nycmathguy]

omg, you are right, he needed to add two irrational numbers a and b to get rational

Ok. I understand what I did wrong. Love those David Cohen textbook questions.