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.

$$20<\dfrac{29}{\sqrt{2}}<21\iff 20 <\dfrac{29}{\sqrt{2}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}}<21 \\ \iff 20<\dfrac{29}{2}\sqrt{2}<21 \\ \iff \dfrac{40}{29}<\sqrt{2}<\dfrac{42}{29}$$
