Question

A pair of irrational numbers whose product is rational are
$\sqrt{3}+3\sqrt{2}$ and $\sqrt{2}-\sqrt{3}$
If true then enter$1$ and if false then enter $0$

Answer 1

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.