How can I prove that $40/29<\sqrt{2}<42/29$ given $20<29/\sqrt{2}<21$ How can I prove that $40/29<\sqrt{2}<42/29$ given $20<29/\sqrt{2}<21$?
I did lot of approaches I obtained in one that: $$\dfrac{29}{42}<\sqrt{2}<\dfrac{29}{10}$$ but couldn't do something other
Thank you.

$20<\frac{29}{\sqrt{2}}<21$ implies $\frac{20}{29}<\frac{1}{\sqrt{2}}<\frac{21}{29}$. So, if we multiply everything by $2$. then,  $\frac{40}{29}<\sqrt{2}<\frac{42}{29}$
