Question

The pair of irrational numbers whose product is rational are $2\sqrt{3}-3\sqrt{2}$ and $2\sqrt{3}+3\sqrt{2}$

• A. True
• B. False

Answer 1

The correct option is B False

To
get the product as rational, the numbers need to have their rational and irrational parts same such that their product $(a+b)(a-b)$ can be solved using the $(a^2-b^2)$ has no irrational part.
Example, the pair of numbers $3-\sqrt{2}$ and $3+\sqrt{2}$ have the product $(3-\sqrt{2})\times (3+\sqrt{2})=9-2=7$ which is a rational number.