Give an example of irrational numbers a and b such that the indicated expression is (a) rational and (b) irrational.?

Taking Q.62 as an example, the question means :
(a) Give an example. In the example, a and b are irrational numbers such that (a + b) is rational.
(b) Give an example. In the example, a and b are irrational numbers such that (a + b) is irrational.


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62.
(a)
Put a = √2 and b = -√2
a + b = √2 + (-√2) = 0
0 is a rational number.

(b)
Put a = √2 and b = 2√2
a + b = √2 + 2√2 = 3√2
3√2 is an irrational number.


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63.
(a)
Put a = √2 and b = 3√2
ab = √2 × 3√2 = 6
6 is a rational number.

(b)
Put a = √2 and b =√3
ab = √2 × √3 = √6
√6 is an irrational number.


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64.
(a)
Put a = 3√2 and b = √2
a/b = (3√2)/(√2) = 3
3 is a rational number.

(b)
Put a = √6 and b = √2
a/b = (√6)/(√2) = √3
√3 is an irrational number.