SOLUTION: Give an example of irrational numbers a and b such the indicated expression is (1) rational and (2) irrational. 1) a + b 2) a

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Question 1197044: Give an example of irrational numbers a and b such the indicated expression is (1) rational and (2) irrational.
1) a + b
2) a - b
3) (a)(b)
4. (a/b)

Answer by ikleyn(52748) (Show Source):
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(1) a = , b = . a and b are irrational, but a+b = 1 is rational. a = , b = . a and b are irrational, and a+b = is irrational. (2) a = , b = . a and b are irrational, but a-b = 1 is rational. a = , b = . a and b are irrational, and a-b = is irrational. (3) a = , b = . a and b are irrational, but a*b = 2 is rational. a = , b = . a and b are irrational, and a*b = is irrational. (4) a = , b = . a and b are irrational, but a/b = 1 is rational. a = , b = . a and b are irrational, and a/b = is irrational.

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SOLUTION: Give an example of irrational numbers a and b such the indicated expression is (1) rational and (2) irrational. 1) a + b 2) a - b 3) (a)(b) 4. (a/b)