1.

Find two irrational numbers such that their sum is a rational number. Can you find two irrational numbers whose product is a rational number.

Answer»

Let the two irrational numbers as 2 + √3 and 3 – √3 

Their sum is 2 + √3 + 3 – 3√3 which is a rational number. 

But the sum of 3 + √5 and 4 – √7 is not a rational number. So the sum of two irrational numbers is either rational or irrational.

Again taking two irrational numbers as π and 3/π their product is √3 and √2 = √3 x √2 which is irrational, So the product of two irrational numbers is either rational or irrational.



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