Q. 13

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

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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