Give two examples to show that the product of two irrational numbers may be arational number.
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
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
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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