# Rational & Irrational Numbers

Discussion in 'Other Pre-University Math' started by nycmathguy, Jul 8, 2021.

1. ### nycmathguy

Joined:
Jun 27, 2021
Messages:
5,386
420
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.

(b) Give an example in which the result of raising an irrational number to a rational power is a rational number.

You say?

nycmathguy, Jul 8, 2021

2. ### MathLover1

Joined:
Jun 27, 2021
Messages:
2,989
2,883
56.

correct

57.

correct

58.
correct

59.
a) correct
b) correct

way to go!

MathLover1, Jul 8, 2021
nycmathguy likes this.

3. ### nycmathguy

Joined:
Jun 27, 2021
Messages:
5,386
420
I'm cooking with gas now. This is a famous Richie line from Happy Days.

nycmathguy, Jul 8, 2021
4. ### HallsofIvy

Joined:
Nov 6, 2021
Messages:
116
50
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.

HallsofIvy, Nov 10, 2021
MathLover1 likes this.
5. ### MathLover1

Joined:
Jun 27, 2021
Messages:
2,989
2,883
omg, you are right, he needed to add two irrational numbers a and b to get rational

MathLover1, Nov 10, 2021

Joined:
Jun 27, 2021
Messages:
5,386