Question Number 183075 by Ml last updated on 19/Dec/22
Answered by BaliramKumar last updated on 19/Dec/22
$${let}\:\:\:\:\:{n}=\mathrm{2}{k} \\ $$$$\:\:\:\:\:{n}^{\mathrm{2}} \:=\:\left(\mathrm{2}{k}\right)^{\mathrm{2}} \:=\:\mathrm{4}{k}^{\mathrm{2}} \:=\:\mathrm{2}\left(\mathrm{2}{k}^{\mathrm{2}} \right)\:=\:\mathrm{2}\left({m}\right)\:\:\:\:{even} \\ $$
Answered by Rasheed.Sindhi last updated on 20/Dec/22
$${n}\equiv\mathrm{0}\left({mod}\:\mathrm{2}\right) \\ $$$$\left({n}\right)^{\mathrm{2}} \equiv\left(\mathrm{0}\right)^{\mathrm{2}} \left({mod}\:\mathrm{2}\right) \\ $$$${n}^{\mathrm{2}} \equiv\mathrm{0}\:\left({mod}\:\mathrm{2}\right) \\ $$$$\therefore{n}\in\mathbb{E}\Rightarrow\:{n}^{\mathrm{2}} \in\mathbb{E} \\ $$