Answer :

Example1:

Take a = 2 + √3 and b=2-√3; a and b are irrational numbers, but their product

ab=(2 + √3)(2-√3)

( ∵ Using (a-b)(a + b)=a ^{ 2 } -b ^{ 2 } )

=(2) ^{ 2 } -(√ 3) ^{ 2 }

=4-3 =1=1/1

Since, it can be represented in form p/q (p=1, q=1) where q≠0 and p;q have no common factor other than 1.

1 is a rational number

Example2:

Take c = √3 and d = -√3; c and d are irrational numbers, but their product cd= √3×-√3=-3

-3 is a rational number.

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