Question Number 44929 by kvbkvb last updated on 06/Oct/18
Commented by ajfour last updated on 06/Oct/18
$${See}\:{Q}.\mathrm{44395} \\ $$
Answered by rahul 19 last updated on 06/Oct/18
$$\frac{\mathrm{1}}{\sqrt{{r}}}\:=\:\frac{\mathrm{1}}{\sqrt{\mathrm{4}}}\:+\:\frac{\mathrm{1}}{\sqrt{\mathrm{2}}} \\ $$$$\Rightarrow\:{r}\:=\:\mathrm{4}\:\left(\:\mathrm{3}−\mathrm{2}\sqrt{\mathrm{2}}\right)\:{units} \\ $$
Answered by ajfour last updated on 06/Oct/18
$${r}\:=\:\frac{{r}_{\mathrm{1}} {r}_{\mathrm{2}} }{\left(\sqrt{{r}_{\mathrm{1}} }+\sqrt{{r}_{\mathrm{2}} }\:\right)^{\mathrm{2}} }\:=\:\frac{\mathrm{4}×\mathrm{2}}{\left(\sqrt{\mathrm{4}}+\sqrt{\mathrm{2}}\right)^{\mathrm{2}} } \\ $$$$\:\:\:=\:\frac{\mathrm{8}}{\mathrm{6}+\mathrm{4}\sqrt{\mathrm{2}}}\:=\:\mathrm{4}\left(\mathrm{3}−\mathrm{2}\sqrt{\mathrm{2}}\:\right). \\ $$